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Question (31)

QN0036801

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

(A) 5
(B) 6
(C) 7
(D) 8

Correct Answer: C

Explanation:

Diagonals of a parallelogram bisect each other. Equating the midpoints of AC and BD gives p = 7.

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Question (32)

QN0036802

If A(1,2), B(5,6), C(9,2), and D(5,−2) are joined in order, the quadrilateral is a

(A) rectangle
(B) square
(C) trapezium
(D) parallelogram but not a square

Correct Answer: B

Explanation:

All four sides are equal and the adjacent sides are perpendicular, so the quadrilateral is a square.

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Question (33)

QN0036803

The points A(−1,−1), B(3,1), C(5,5), and D(1,3) form a

(A) square
(B) rectangle
(C) rhombus
(D) trapezium

Correct Answer: C

Explanation:

All four sides are equal, while the diagonals are unequal. Hence the quadrilateral is a rhombus.

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Question (34)

QN0036804

The coordinates A(0,0), B(4,3), and C(8,0) form an isosceles triangle because

(A) AB=AC
(B) AB=BC
(C) AC=BC
(D) all three sides are equal

Correct Answer: B

Explanation:

AB = 5, BC = 5 and AC = 8. Hence AB = BC, so the triangle is isosceles.

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Question (35)

QN0036805

If A(1,1), B(4,5), and C(8,2), then AB² + BC² is

(A) 41
(B) 50
(C) 58
(D) 65

Correct Answer: B

Explanation:

AB² = 3²+4² = 25 and BC² = 4²+(−3)² = 25. Therefore AB²+BC² = 50.

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Question (36)

QN0036806

The points A(0,0), B(3,4), and C(6,0) form a triangle whose side lengths are

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

Correct Answer: B

Explanation:

AB = 5, BC = 5 and AC = 6. Therefore the side lengths are 5,5,6.

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Question (37)

QN0036807

If the distance between A(2,3) and B(8,y) is √61, then y can be

(A) 10 or −4
(B) 8 or −2
(C) 9 or −3
(D) 7 or −1

Correct Answer: B

Explanation:

61 = 6²+(y−3)², so (y−3)²=25 and y=8 or −2.

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Question (38)

QN0036808

If A(2,3) and B(8,9), the point which divides AB in the ratio 1:2 is

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

Correct Answer: A

Explanation:

P = ((1×8+2×2)/3, (1×9+2×3)/3) = (4,5).

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Question (39)

QN0036809

The point P(5,5) is the midpoint of A(2,3) and B(x,y). The value of x+y is

(A) 12
(B) 13
(C) 14
(D) 15

Correct Answer: D

Explanation:

x=8 and y=7 from the midpoint formula. Therefore x+y=15.

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Question (40)

QN0036810

The point P divides A(2,4) and B(8,10) in the ratio 1:1. Which statement is correct?

(A) P=(4,6)
(B) P=(5,7)
(C) P=(6,8)
(D) P=(3,5)

Correct Answer: B

Explanation:

Ratio 1:1 means P is the midpoint. P = ((2+8)/2,(4+10)/2) = (5,7).

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Question (31)

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

Explanation:

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Question (32)

If A(1,2), B(5,6), C(9,2), and D(5,−2) are joined in order, the quadrilateral is a

Explanation:

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Question (33)

The points A(−1,−1), B(3,1), C(5,5), and D(1,3) form a

Explanation:

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Question (34)

The coordinates A(0,0), B(4,3), and C(8,0) form an isosceles triangle because

Explanation:

Link:

Question (35)

If A(1,1), B(4,5), and C(8,2), then AB² + BC² is

Explanation:

Link:

Question (36)

The points A(0,0), B(3,4), and C(6,0) form a triangle whose side lengths are

Explanation:

Link:

Question (37)

If the distance between A(2,3) and B(8,y) is √61, then y can be

Explanation:

Link:

Question (38)

If A(2,3) and B(8,9), the point which divides AB in the ratio 1:2 is

Explanation:

Link:

Question (39)

The point P(5,5) is the midpoint of A(2,3) and B(x,y). The value of x+y is

Explanation:

Link:

Question (40)

The point P divides A(2,4) and B(8,10) in the ratio 1:1. Which statement is correct?

Explanation:

Link:

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