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Question (21)

QN0036791

The point dividing A(2,3) and B(12,8) internally in the ratio 2:3 is

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

Correct Answer: B

Explanation:

P = ((2×12+3×2)/5, (2×8+3×3)/5) = (6,5).

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Question (22)

QN0036792

The point P dividing A(−2,4) and B(8,−6) internally in the ratio 1:4 is

(A) (0,2)
(B) (0,1)
(C) (2,0)
(D) (1,0)

Correct Answer: A

Explanation:

P = ((1×8+4×(−2))/5, (1×(−6)+4×4)/5) = (0,2).

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Question (23)

QN0036793

The two points of trisection of the line segment joining A(1,1) and B(10,7) are

(A) (4,3) and (7,5)
(B) (3,2) and (6,4)
(C) (4,2) and (7,6)
(D) (3,3) and (6,5)

Correct Answer: A

Explanation:

The trisection points divide AB in ratios 1:2 and 2:1, giving (4,3) and (7,5).

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Question (24)

QN0036794

The point dividing A(4,−2) and B(10,7) internally in the ratio 2:1 is

(A) (8,4)
(B) (8,8/3)
(C) (7,4)
(D) (6,3)

Correct Answer: A

Explanation:

P = ((2×10+4)/3, (2×7−2)/3) = (8,4).

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Question (25)

QN0036795

If P(3,4) is the midpoint of A(1,2) and B(x,y), then B is

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

Correct Answer: A

Explanation:

From the midpoint formula, 3=(1+x)/2 and 4=(2+y)/2, giving x=5 and y=6.

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Question (26)

QN0036796

If P(4,5) divides A(1,2) and B(10,8), then AP:PB is

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

Correct Answer: A

Explanation:

Using the section formula with P(4,5) gives m1:m2 = 1:2.

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Question (27)

QN0036797

The point (0,3) divides the segment joining A(5,−6) and B(−1,−4) in the ratio

(A) 5:1
(B) 1:5
(C) 2:5
(D) 5:2

Correct Answer: A

Explanation:

Since the point lies on the y-axis, its x-coordinate is zero. Applying the section formula gives the ratio 5:1.

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Question (28)

QN0036798

The point P(2,3) lies on the line segment joining A(−1,0) and B(8,9). The ratio AP:PB is

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

Correct Answer: A

Explanation:

AP = 3√2 and PB = 6√2, so AP:PB = 1:2.

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Question (29)

QN0036799

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

(A) −1
(B) 0
(C) 1
(D) 2

Correct Answer: A

Explanation:

y = (1×5 + 2×(−4))/3 = −1.

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Question (30)

QN0036800

The point dividing A(−6,4) and B(3,−5) internally in the ratio 2:1 is

(A) (0,−2)
(B) (0,1)
(C) (−1,−2)
(D) (1,−1)

Correct Answer: A

Explanation:

P = ((2×3−6)/3, (2×(−5)+4)/3) = (0,−2).

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Question (21)

The point dividing A(2,3) and B(12,8) internally in the ratio 2:3 is

Explanation:

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Question (22)

The point P dividing A(−2,4) and B(8,−6) internally in the ratio 1:4 is

Explanation:

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Question (23)

The two points of trisection of the line segment joining A(1,1) and B(10,7) are

Explanation:

Link:

Question (24)

The point dividing A(4,−2) and B(10,7) internally in the ratio 2:1 is

Explanation:

Link:

Question (25)

If P(3,4) is the midpoint of A(1,2) and B(x,y), then B is

Explanation:

Link:

Question (26)

If P(4,5) divides A(1,2) and B(10,8), then AP:PB is

Explanation:

Link:

Question (27)

The point (0,3) divides the segment joining A(5,−6) and B(−1,−4) in the ratio

Explanation:

Link:

Question (28)

The point P(2,3) lies on the line segment joining A(−1,0) and B(8,9). The ratio AP:PB is

Explanation:

Link:

Question (29)

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

Explanation:

Link:

Question (30)

The point dividing A(−6,4) and B(3,−5) internally in the ratio 2:1 is

Explanation:

Link:

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