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Question (41)

QN0036811

A point P divides A(−4,5) and B(8,−1) in the ratio 2:1. The x-coordinate of P is

(A) 2
(B) 3
(C) 4
(D) 5

Correct Answer: C

Explanation:

x = (2×8 + 1×(−4))/3 = 4.

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Question (42)

QN0036812

If the midpoint of A(x,4) and B(6,8) is (5,6), then x is

(A) 2
(B) 3
(C) 4
(D) 5

Correct Answer: C

Explanation:

5 = (x+6)/2, so x = 4.

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Question (43)

QN0036813

The point P(2,4) divides A(−4,−2) and B(8,10) in the ratio

(A) 1:2
(B) 2:1
(C) 1:1
(D) 3:1

Correct Answer: C

Explanation:

P = ((−4+8)/2,(−2+10)/2) = (2,4), so P is the midpoint and the ratio is 1:1.

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Question (44)

QN0036814

The point which divides A(2,2) and B(10,10) into four equal parts and is nearest to A is

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

Correct Answer: A

Explanation:

The first quarter point divides AB in the ratio 1:3. Its coordinates are (4,4).

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Question (45)

QN0036815

If A(1,7), B(4,2), C(−1,−1), and D(−4,4) are the vertices of a square, the square of the length of each side is

(A) 25
(B) 34
(C) 49
(D) 68

Correct Answer: B

Explanation:

AB² = (1−4)²+(7−2)² = 9+25 = 34.

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Question (46)

QN0036816

If A(2,−3) and B(6,5), then the midpoint of AB lies in

(A) First quadrant
(B) Second quadrant
(C) Third quadrant
(D) Fourth quadrant

Correct Answer: A

Explanation:

Midpoint = ((2+6)/2,(−3+5)/2) = (4,1), which lies in the first quadrant.

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Question (47)

QN0036817

A line segment has endpoints A(−5,3) and B(7,−5). The midpoint of the segment is

(A) (1,−1)
(B) (−1,1)
(C) (2,−1)
(D) (1,1)

Correct Answer: A

Explanation:

Midpoint = ((−5+7)/2,(3−5)/2) = (1,−1).

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Question (48)

QN0036818

If A(6,1), B(8,2), C(9,4), and D(p,3) are consecutive vertices of a parallelogram, then p equals

(A) 5
(B) 6
(C) 7
(D) 9

Correct Answer: C

Explanation:

Since the diagonals of a parallelogram bisect each other, equating the midpoint coordinates gives p = 7.

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Question (49)

QN0036819

The points A(1,7), B(4,2), C(−1,−1), and D(−4,4) form a square. What is the square of the length of each side?

(A) 25
(B) 34
(C) 49
(D) 68

Correct Answer: B

Explanation:

AB² = (1−4)²+(7−2)² = 9+25 = 34. All four sides have the same squared length.

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Question (50)

QN0036820

The points P(3,2), Q(−2,−3), and R(2,3) form a right triangle. The right angle is at

(A) P
(B) Q
(C) R
(D) None of these

Correct Answer: A

Explanation:

PQ²=50, PR²=2 and QR²=52. Since PQ²+PR²=QR², the right angle is at P.

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Question (41)

A point P divides A(−4,5) and B(8,−1) in the ratio 2:1. The x-coordinate of P is

Explanation:

Link:

Question (42)

If the midpoint of A(x,4) and B(6,8) is (5,6), then x is

Explanation:

Link:

Question (43)

The point P(2,4) divides A(−4,−2) and B(8,10) in the ratio

Explanation:

Link:

Question (44)

The point which divides A(2,2) and B(10,10) into four equal parts and is nearest to A is

Explanation:

Link:

Question (45)

If A(1,7), B(4,2), C(−1,−1), and D(−4,4) are the vertices of a square, the square of the length of each side is

Explanation:

Link:

Question (46)

If A(2,−3) and B(6,5), then the midpoint of AB lies in

Explanation:

Link:

Question (47)

A line segment has endpoints A(−5,3) and B(7,−5). The midpoint of the segment is

Explanation:

Link:

Question (48)

If A(6,1), B(8,2), C(9,4), and D(p,3) are consecutive vertices of a parallelogram, then p equals

Explanation:

Link:

Question (49)

The points A(1,7), B(4,2), C(−1,−1), and D(−4,4) form a square. What is the square of the length of each side?

Explanation:

Link:

Question (50)

The points P(3,2), Q(−2,−3), and R(2,3) form a right triangle. The right angle is at

Explanation:

Link:

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