Geometry Study Resources for Competitive Exams

Geometry

Q. If angle C is 30 degrees and is one of the corresponding angles formed by a transversal intersecting two parallel lines, what is the measure of the other corresponding angle?

A. 30 degrees
B. 150 degrees
C. 90 degrees
D. 60 degrees

Solution

Corresponding angles are equal when a transversal intersects two parallel lines. Therefore, the other corresponding angle also measures 30 degrees.

Correct Answer: A — 30 degrees

Learn More →

Q. If angle C is a corresponding angle to angle D and angle D measures 85 degrees, what is the measure of angle C?

A. 85 degrees
B. 95 degrees
C. 75 degrees
D. 180 degrees

Solution

Corresponding angles are equal, so angle C also measures 85 degrees.

Correct Answer: A — 85 degrees

Learn More →

Q. If angle X and angle Y are complementary and angle X measures 35°, what is the measure of angle Y?

A. 45°
B. 55°
C. 65°
D. 75°

Solution

Complementary angles sum to 90°. Therefore, angle Y = 90° - 35° = 55°.

Correct Answer: B — 55°

Learn More →

Q. If line A has a slope of 4 and line B is perpendicular to line A, what is the slope of line B?

A. -1/4
B. 1/4
C. -4
D. 4

Solution

The slopes of perpendicular lines are negative reciprocals. The negative reciprocal of 4 is -1/4.

Correct Answer: A — -1/4

Learn More →

Q. If one angle of a triangle is 50 degrees and another is 60 degrees, what is the measure of the third angle?

A. 70 degrees
B. 80 degrees
C. 90 degrees
D. 100 degrees

Solution

The third angle can be found by subtracting the sum of the other two angles from 180 degrees: 180 - (50 + 60) = 70 degrees.

Correct Answer: A — 70 degrees

Learn More →

Q. If one angle of a triangle is 90 degrees and the other two angles are equal, what are the measures of the other two angles?

A. 30 degrees
B. 45 degrees
C. 60 degrees
D. 75 degrees

Solution

In a triangle, the sum of the angles is 180 degrees. If one angle is 90 degrees, the remaining two angles must sum to 90 degrees. Since they are equal, each must be 45 degrees.

Correct Answer: B — 45 degrees

Learn More →

Q. If point A is at (1, 2) and point B is at (4, 6), what is the section formula for point C that divides AB in the ratio 1:2?

A. (2, 3)
B. (3, 4)
C. (2.5, 4)
D. (3.5, 5)

Solution

Using the section formula: C = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)) where m=1, n=2. C = ((1*4 + 2*1)/(1+2), (1*6 + 2*2)/(1+2)) = (3, 4).

Correct Answer: B — (3, 4)

Learn More →

Q. If point A is at (1, 2) and point B is at (4, 6), what is the section formula for point P that divides AB in the ratio 1:2?

A. (2, 3)
B. (3, 4)
C. (1.5, 2.5)
D. (2.5, 3.5)

Solution

Using the section formula: P = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)) = ((1*4 + 2*1)/(1+2), (1*6 + 2*2)/(1+2)) = (3, 4).

Correct Answer: B — (3, 4)

Learn More →

Q. If point A is at (1, 2) and point B is at (4, 6), what is the section formula ratio if point C divides AB in the ratio 1:2?

A. (2, 4)
B. (3, 5)
C. (2.5, 4)
D. (3, 4)

Solution

Using the section formula: C = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)) where m=1, n=2. C = ((1*4 + 2*1)/(1+2), (1*6 + 2*2)/(1+2)) = (2.67, 4).

Correct Answer: B — (3, 5)

Learn More →

Q. If point A is at (1, 2) and point B is at (4, 6), what is the section formula to find point C that divides AB in the ratio 1:2?

A. (2, 4)
B. (3, 5)
C. (2.5, 4)
D. (3.5, 5)

Solution

Using the section formula: C = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)) = ((1*4 + 2*1)/(1+2), (1*6 + 2*2)/(1+2)) = (3, 5).

Correct Answer: B — (3, 5)

Learn More →

Q. If point A is at (2, 3) and point B is at (8, 7), what is the midpoint M of segment AB?

A. (5, 5)
B. (4, 5)
C. (6, 5)
D. (5, 4)

Solution

Midpoint M = ((x1 + x2)/2, (y1 + y2)/2) = ((2 + 8)/2, (3 + 7)/2) = (5, 5).

Correct Answer: A — (5, 5)

Learn More →

Q. If point A is at (3, 5) and point B is at (9, 1), what is the coordinates of point P that divides AB in the ratio 2:3?

A. (5.4, 3.6)
B. (6, 4)
C. (5, 3)
D. (4, 2)

Solution

Using the section formula: P = ((2*9 + 3*3)/(2+3), (2*1 + 3*5)/(2+3)) = (5.4, 3.6).

Correct Answer: A — (5.4, 3.6)

Learn More →

Q. If point A(2, 3) and point B(8, 7) are endpoints of a line segment, what is the midpoint M?

A. (5, 5)
B. (4, 5)
C. (6, 5)
D. (5, 4)

Solution

Midpoint M = ((x1 + x2)/2, (y1 + y2)/2) = ((2 + 8)/2, (3 + 7)/2) = (5, 5).

Correct Answer: A — (5, 5)

Learn More →

Q. If point A(2, 3) and point B(8, 7) are endpoints of a line segment, what is the midpoint M of AB?

A. (5, 5)
B. (4, 5)
C. (6, 5)
D. (5, 4)

Solution

Midpoint M = ((x1 + x2)/2, (y1 + y2)/2) = ((2 + 8)/2, (3 + 7)/2) = (5, 5).

Correct Answer: A — (5, 5)

Learn More →

Q. If point A(2, 3) and point B(8, 7) are given, what is the midpoint M of segment AB?

A. (5, 5)
B. (4, 5)
C. (6, 5)
D. (5, 4)

Solution

Using the midpoint formula: M = ((x1 + x2)/2, (y1 + y2)/2) = ((2 + 8)/2, (3 + 7)/2) = (5, 5).

Correct Answer: A — (5, 5)

Learn More →

Q. If point A(2, 3) and point B(8, 7) are the endpoints of a line segment, what is the midpoint M of AB?

A. (5, 5)
B. (4, 5)
C. (6, 5)
D. (5, 4)

Solution

Midpoint M = ((x1 + x2)/2, (y1 + y2)/2) = ((2 + 8)/2, (3 + 7)/2) = (5, 5).

Correct Answer: A — (5, 5)

Learn More →

Q. If point C divides the segment AB in the ratio 2:3, where A(1, 2) and B(6, 8), what are the coordinates of point C?

A. (3.0, 4.0)
B. (4.0, 5.0)
C. (2.0, 3.0)
D. (5.0, 6.0)

Solution

Using the section formula: C = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)) = ((2*6 + 3*1)/(2+3), (2*8 + 3*2)/(2+3)) = (4.0, 5.0).

Correct Answer: B — (4.0, 5.0)

Learn More →

Q. If point C is at (0, 0) and point D is at (6, 8), what is the length of segment CD?

A. 8
B. 10
C. 6
D. 12

Solution

Using the distance formula: d = √((6 - 0)² + (8 - 0)²) = √(36 + 64) = √100 = 10.

Correct Answer: B — 10

Learn More →

Q. If point C is at (2, 3) and point D is at (10, 7), what is the coordinates of point E that divides CD in the ratio 1:3?

A. (5, 4)
B. (4, 5)
C. (6, 5)
D. (7, 6)

Solution

Using the section formula: E = ((1*10 + 3*2)/(1+3), (1*7 + 3*3)/(1+3)) = (5, 4).

Correct Answer: A — (5, 4)

Learn More →

Q. If point C is at (3, 5) and point D is at (9, 1), what is the coordinates of the point that divides CD in the ratio 2:3?

A. (5.4, 3.2)
B. (6, 3)
C. (4.5, 4)
D. (5, 4)

Solution

Using the section formula: P = ((2*9 + 3*3)/(2+3), (2*1 + 3*5)/(2+3)) = (5.4, 3.2).

Correct Answer: A — (5.4, 3.2)

Learn More →

Q. If point C is at (4, 5) and point D is at (10, 15), what is the distance between C and D?

A. 10
B. 11.18
C. 12
D. 9.22

Solution

Using the distance formula: d = √((10 - 4)² + (15 - 5)²) = √(36 + 100) = √136 ≈ 11.18.

Correct Answer: B — 11.18

Learn More →

Q. If point C is at (5, 5) and point D is at (5, 10), what is the distance between points C and D?

A. 5
B. 10
C. 15
D. 20

Solution

Distance = |y2 - y1| = |10 - 5| = 5.

Correct Answer: A — 5

Learn More →

Q. If point C(0, 0) and point D(6, 8) are endpoints of a line segment, what is the length of CD?

A. 10
B. 8
C. 6
D. 12

Solution

Using the distance formula: d = √((6 - 0)² + (8 - 0)²) = √(36 + 64) = √100 = 10.

Correct Answer: A — 10

Learn More →

Q. If point C(0, 0) and point D(6, 8) are the endpoints of a line segment, what is the length of CD?

A. 8.0
B. 10.0
C. 6.0
D. 7.0

Solution

Using the distance formula: d = √((6 - 0)² + (8 - 0)²) = √(36 + 64) = √100 = 10.0.

Correct Answer: B — 10.0

Learn More →

Q. If point C(1, 1) divides the line segment joining points A(0, 0) and B(4, 4) in the ratio k:1, what is the value of k?

A. 1
B. 2
C. 3
D. 4

Solution

Using the section formula, C = ((kx2 + x1)/(k+1), (ky2 + y1)/(k+1)). Setting C(1, 1) gives k = 1.

Correct Answer: B — 2

Learn More →

Q. If point C(1, 2) and point D(7, 8) are given, what is the coordinates of the point that divides CD in the ratio 3:2?

A. (4, 5)
B. (5, 6)
C. (3, 4)
D. (6, 7)

Solution

Using the section formula: P = ((3*7 + 2*1)/(3+2), (3*8 + 2*2)/(3+2)) = (4, 5).

Correct Answer: A — (4, 5)

Learn More →

Q. If point C(4, 5) is the midpoint of segment AB, and A is at (2, 3), what are the coordinates of point B?

A. (6, 7)
B. (8, 9)
C. (4, 5)
D. (2, 3)

Solution

Using the midpoint formula: B = (2*C - A) = (2*4 - 2, 2*5 - 3) = (6, 7).

Correct Answer: A — (6, 7)

Learn More →

Q. If point D divides the line segment joining points (2, 5) and (8, 9) in the ratio 3:1, what are the coordinates of point D?

A. (5, 7)
B. (6, 8)
C. (4, 6)
D. (7, 8)

Solution

Using the section formula: D = ((3*8 + 1*2)/(3+1), (3*9 + 1*5)/(3+1)) = (5, 7).

Correct Answer: A — (5, 7)

Learn More →

Q. If point D divides the segment AB with A(2, 3) and B(8, 7) in the ratio 2:3, what are the coordinates of D?

A. (4.8, 5.2)
B. (5.2, 4.8)
C. (6, 5)
D. (5, 5)

Solution

Using the section formula: D = ((2*8 + 3*2)/(2+3), (2*7 + 3*3)/(2+3)) = (4.8, 5.2).

Correct Answer: A — (4.8, 5.2)

Learn More →

Q. If point D is at (5, 5) and point E is at (1, 1), what is the distance DE?

A. 4
B. 5
C. 6
D. 7

Solution

Using the distance formula: d = √((5 - 1)² + (5 - 1)²) = √(16 + 16) = √32 = 4√2 ≈ 5.66.

Correct Answer: B — 5

Learn More →

Showing 211 to 240 of 1419 (48 Pages)

Geometry

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?