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MCQ in Geometry Part 3 | Mathematics Board Exam

MCQs in Geometry Part 3

This is the Multiple Choice Questions Part 3 of the Series in Geometry topic in Engineering Mathematics. In Preparation for the ECE Board Exam make sure to expose yourself and familiarize in each and every questions compiled here taken from various sources including but not limited to past Board Examination Questions in Engineering Mathematics, Mathematics Books, Journals and other Mathematics References.

MCQ Topic Outline included in Mathematics Board Exam Syllabi

  • MCQ in Lines and Planes | MCQ in lane figures | MCQ in Application of Cavalier’s, Pappus and Prismodial Theorems | MCQ in Coordinate in Space | MCQ in Quadratic Surfaces | MCQ in Mensuration | MCQ in Plane Geometry | MCQ in Solid Geometry | MCQ in Spherical Geometry | MCQs in Analytical Geometry

Continue Practice Exam Test Questions Part 3 of the Series

MCQ in Geometry Part 2 | Mathematics Board Exam

Choose the letter of the best answer in each questions.
101. Find the distance between the lines 3x + y – 12 = 0 and 3x + y – 4 = 0.

A. 16/sqrt(10)

B. 12/sqrt(10)

C. 4/sqrt(10)

D. 8/sqrt(10)

View Answer:

Answer: Option D

Solution:

102. What is the length of the line with a slope of 4/3 from a point (6, 4) to the y-axis?

A. 10

B. 25

C. 50

D. 75

View Answer:

Answer: Option A

Solution:

103. Find the slope of the line defined by y – x = 5.

A. 1

B. 1/4

C. -1/2

D. 5 + x

View Answer:

Answer: Option A

Solution:

104. What is the slope of the line 3x + 2y + 1 = 0?

A. 3/2

B. 2/3

C. -3/2

D. -2/3

View Answer:

Answer: Option C

Solution:

105. In a Cartesian coordinates, the vertices of a triangle are defined by the following points: (-2, 0), (4, 0) and (3, 3). What is the area?

A. 8 sq. units

B. 9 sq. units

C. 10 sq. units

D. 11 sq. units

View Answer:

Answer: Option B

Solution:

106. Given three vertices of a triangle whose coordinates are A (1, 1), B (3, -3) and (5, -3). Find the area of the triangle.

A. 3

B. 4

C. 5

D. 6

View Answer:

Answer: Option B

Solution:

107. In a Cartesian coordinates, the vertices of a square are: (1, 1), (0, 8) (4, 5) and (-3, 4). What is the area?

A. 20 sq. units

B. 30 sq. units

C. 25 sq. units

D. 35 sq. units

View Answer:

Answer: Option C

Solution:

108. A line passes thru (1, -3) and (-4, 2). Write the equation of the line in slope-initial form

A. y – 4 = x

B. y = -x – 2

C. y = x – 4

D. y – 2 = x

View Answer:

Answer: Option B

Solution:

109. What is the x-intercept of the line passing through (1, 4) and (4, 1)?

A. 4.5

B. 5

C. 4

D. 6

View Answer:

Answer: Option B

Solution:

110. Find the equation of a straight line with a slope of 3 and a y-intercept of 1.

A. 3x + y – 1 = 0

B. 3x – y + 1 = 0

C. x + 3y + 1 = 0

D. x – 3y – 1 = 0

View Answer:

Answer: Option B

Solution:

111. If the points (-2, 3), (x, y) and (-3, 5) lie on a straight line, then the equation of the line is _________.

A. x – 2y – 1 = 0

B. 2x + y – 1 = 0

C. x + 2y – 1 = 0

D. 2x + y + 1 = 0

View Answer:

Answer: Option D

Solution:

112. The equation of a line that intercepts the x-axis at x = 4 and the y-axis at y = -6 is,

A. 3x + 2y = 12

B. 2x – 3y = 12

C. 3x – 2y = 12

D. 2x – 3y = 12

View Answer:

Answer: Option C

Solution:

113. A line with an inclination of 45° passes through (-5/2, 9/2). What is the x-coordinate of a point on the line if its corresponding y-coordinate is 6?

A. 6

B. 7

C. 8

D. 9

View Answer:

Answer: Option C

Solution:

114. Find the equation of the line passing through the origin and with a slope of 6?

A. y – 6x = 0

B. y = -6

C. x + y = -6

D. 6x + y = 0

View Answer:

Answer: Option A

Solution:

115. Find the equation of the line if the x-intercept and y-intercept are -2 and 4, respectively.

A. y – 2x – 4 = 0

B. y + 2x – 4 = 0

C. y – 2x + 4 = 0

D. y + 2x + 4 = 0

View Answer:

Answer: Option B

Solution:

116. Determine B such that 3x + 2y – 7 = 0 is perpendicular to 2x – By + 2 = 0.

A. 5

B. 4

C. 3

D. 2

View Answer:

Answer: Option C

Solution:

117. The line 2x – 3y + 2 = 0 is perpendicular to another line L1 of unknown equation. Find the slope of L1.

A. 3/2

B. -3/2

C. 2/3

D. -2/3

View Answer:

Answer: Option B

Solution:

118. A line through (-5, 2) and (1, -4) is perpendicular to the line through (x, -7) and (8, 7). Find x.

A. -4

B. -5

C. -6

D. -19/3

View Answer:

Answer: Option C

Solution:

119. What is the equation of the line that passes through (4, 0) and is parallel to the line x – y – 2 = 0?

A. x – y + 4 = 0

B. x + y + 4 = 0

C. x – y – 4 = 0

D. x – y = 0

View Answer:

Answer: Option C

Solution:

120. Find the equation of the line through point (3, 1) and is perpendicular to the line x + 5y + 5 = 0.

A. 5x – 2y = 14

B. 5x – y = 14

C. 2x – 5y = 14

D. 2x + 5y = 14

View Answer:

Answer: Option B

Solution:

121. Find the equation of the perpendicular bisector of the line joining (5, 0) and (-7, 3)

A. 8x + 2y + 11 = 0

B. 8x – 2y + 11 = 0

C. 8x – y + 11 = 0

D. 8x + y + 11 = 0

View Answer:

Answer: Option B

Solution:

122. Which of the following lines is parallel to the line 3x – 2y + 6 = 0?

A. 3x + 2y – 12 = 0

B. 4x – 9y = 6

C. 12x + 18y = 15

D. 15x – 10y – 9 = 0

View Answer:

Answer: Option D

Solution:

123. The equation of the line through (-3, 5) parallel to 7x + 2y -4 = 0 is

A. 7x + 2y + 31 = 0

B. 7x – 2y + 30 = 0

C. 7x + 2y – 4 = 0

D. 2x + 7y + 30 = 0

View Answer:

Answer: Option A

Solution:

124. What is the equation of the line joining the points (3, -2) and (-7, 6)?

A. 2x + 3y = 0

B. 4x – 5y = 22

C. 4x + 5y = 2

D. 5x + 4y = 7

View Answer:

Answer: Option C

Solution:

125. What is the equation of the line passing through (-2, 6) with the x-intercept half the y-intercept?

A. x – y = 6

B. 2x + 2y + 2 = 0

C. 3x – y + 2 = 0

D. 2x + y – 2 = 0

View Answer:

Answer: Option D

Solution:

126. Find the slope of a line having a parametric equation of x = 2 + t and y = 5 – 3t.

A. 2

B. 3

C. -2

D. -3

View Answer:

Answer: Option D

Solution:

127. Find the slope of the line having a parametric equation y = 4t + 6 and x = t + 1.

A. 1

B. 2

C. 3

D. 4

View Answer:

Answer: Option D

Solution:

128. Two vertices of a triangle are (2, 4) and (-2, 3) and the area is 2 square units, the locus of the third vertex is

A. 4x – y = 14

B. 4x + 4y = 14

C. x + 4y = 12

D. x – 4y = -14

View Answer:

Answer: Option D

Solution:

129. Find the area of the triangle which the line 2x – 3y + 6 = 0 forms with the coordinate axis.

A. 3

B. 4

C. 5

D. 2

View Answer:

Answer: Option A

Solution:

130. A line passes through point (2, 2). Find the length equation of the line if the length of the line segment intercepted by the coordinates axed is the square root of 5.

A. 2x + y – 2 = 0

B. 2x – y – 2 = 0

C. 2x – y + 2 = 0

D. 2x + y + 2 = 0

View Answer:

Answer: Option B

Solution:

131. What is the radius of the circle x2 + y2 – 6y = 0?

A. 2

B. 3

C. 4

D. 5

View Answer:

Answer: Option B

Solution:

132. What are the coordinates of the center of the curve x2 + y2 – 2x – 4y – 31 = 0?

A. (-1, -1)

B. (-2, -2)

C. (1, 2)

D. (2, 1)

View Answer:

Answer: Option C

Solution:

133. A circle whose equation is x2 + y2 + 4x + 6y – 23 = 0 has its center at:

A. (2, 3)

B. (3, 2)

C. -3, 2)

D. (-2, -3)

View Answer:

Answer: Option D

Solution:

134. What is the radius of a circle with the ff. Equation: x2 – 6x + y2 – 4y – 12 = 0

A. 3.46

B. 7

C. 5

D. 6

View Answer:

Answer: Option C

Solution:

135. The diameter of a circle described by 9x2 + 9y2 = 16 is

A. 4/3

B. 16/9

C. 8/3

D. 4

View Answer:

Answer: Option C

Solution:

136. How far from the y-axis is the center of the curve 2x2 + 2y2 + 10x – 6y – 55 = 0?

A. -2.5

B. -3.0

C. -2.75

D. -3.25

View Answer:

Answer: Option A

Solution:

137. What is the distance between the centers of the circles x2 + y2 + 2x + 4y – 3 = 0 and x2 + y2 -8x -6y + 7 = 0?

A. 7.07

B. 7.77

C. 8.07

D. 7.87

View Answer:

Answer: Option A

Solution:

138. The shortest distance from A(3, 8) to the circle x2 + y2 + 4x – 6y = 12 is equal to

A. 2.1

B. 2.3

C. 2.5

D. 2.7

View Answer:

Answer: Option B

Solution:

139. The equation x2 + y2 – 4x + 2y – 20 = 0 describes:

A. A circle of radius 5 centered at the origin.

B. An ellipse centered at (2, -1)

C. A sphere centered at the origin.

D. A circle of radius 5 centered at (2, -1)

View Answer:

Answer: Option D

Solution:

140. The center of a circle is at (1, 1) and one point on its circumference is (-1, -3.) Find the other end of the diameter through (-1, -3).

A. (2, 4)

B. (3, 5)

C. (3, 6)

D. (1, 3)

View Answer:

Answer: Option B

Solution:

141. Find the area (in square units) of the circle whose equation is x2 + y2 = 6x – 8y.

A. 20π

B. 22π

C. 25π

D. 27π

View Answer:

Answer: Option C

Solution:

142. Determine the equation of the circle whose radius is 5, center on the line x = 2 and tangent to the line 3x – 4y + 11 = 0.

A. (x – 2)2 + (y – 2)2 = 5

B. (x – 2)2 + (y + 2)2 = 25

C. (x – 2)2 + (y + 2)2 = 5

D. (x – 2)2 + (y – 2)2 = 25

View Answer:

Answer: Option B

Solution:

143. Find the equation of the circle with the center at (-4, 5) and tangent to the line 2x + 7y – 10 = 0.

A. x2 + y2 + 8x – 10y – 12 = 0

B. x2 + y2 + 8x – 10y + 12 = 0

C. x2 + y2 + 8x + 10y – 12 = 0

D. x2 + y2 + 8x + 10y + 12 = 0

View Answer:

Answer: Option C

Solution:

144. Find the value of k for which the equation x2 + y2 + 4x – 2y – k = 0 represents a point circle.

A. 5

B. 6

C. -6

D. -5

View Answer:

Answer: Option A

Solution:

145. 3x2 + 2x – 5y + 7 = 0. Determine the curve.

A. Parabola

B. Ellipse

C. Circle

D. Hyperbola

View Answer:

Answer: Option A

Solution:

146. The focus of the parabola y2 = 4x is at:

A. (4, 0)

B. (0, 4)

C. (3, 0)

D. (0, 3)

View Answer:

Answer: Option A

Solution:

147. Where is the vertex of the parabola x2 = 4(y – 2)?

A. (2, 0)

B. (0, 2)

C. (3, 0)

D. (0, 3)

View Answer:

Answer: Option B

Solution:

148. Find the equation of the directrix of the parabola y2 = 16x.

A. x = 2

B. x = -2

C. x = 4

D. x = -4

View Answer:

Answer: Option D

Solution:

149. Given the equation of a parabola 3x + 2y2 – 4y + 7 = 0. Locate its vertex.

A. (5/3, 1)

B. (5/3, -1)

C. (-5/3, -1)

D. (-5/3, 1)

View Answer:

Answer: Option D

Solution:

150. In the equation y = -x2 + x +1, where is the curve facing?

A. upward

B. facing left

C. facing right

D. downward

View Answer:

Answer: Option D

Solution:

Online Question and Answer in Geometry Series

Following is the list of multiple choice questions in this brand new series:

MCQ in Geometry
PART 1: MCQ from Number 1 – 50                                                               Answer key: PART 1
PART 2: MCQ from Number 51 – 100                                                           Answer key: PART 2
PART 3: MCQ from Number 101 – 150                                                         Answer key: PART 3
PART 4: MCQ from Number 151 – 200                                                         Answer key: PART 4
PART 5: MCQ from Number 201 – 250                                                         Answer key: PART 5
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