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Question (11)

QN0036781

The points A(0,0), B(6,0), and C(6,8) form a

(A) right-angled triangle
(B) equilateral triangle
(C) isosceles triangle with no right angle
(D) straight line

Correct Answer: A

Explanation:

AB = 6, BC = 8 and AC = 10. Since 6² + 8² = 10², the triangle is right-angled.

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Question (12)

QN0036782

The points A(2,1), B(6,4), and C(10,7) are

(A) collinear
(B) vertices of a right triangle
(C) vertices of an equilateral triangle
(D) vertices of an isosceles triangle

Correct Answer: A

Explanation:

AB = 5, BC = 5 and AC = 10. Since AB + BC = AC, the points are collinear.

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Question (13)

QN0036783

The point P(x,4) is equidistant from A(2,1) and B(6,1). The value of x is

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

Correct Answer: C

Explanation:

Equating squared distances gives (x−2)² = (x−6)², hence x = 4.

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Question (14)

QN0036784

A point P(x,y) is equidistant from A(2,3) and B(6,7). Which relation is satisfied by x,y?

(A) x+y=5
(B) x−y=1
(C) x+y=9
(D) x−y=5

Correct Answer: C

Explanation:

Equating the squared distances and simplifying gives x + y = 9.

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Question (15)

QN0036785

The point on the y-axis equidistant from A(3,4) and B(−5,2) is

(A) (0,2)
(B) (0,3)
(C) (0,5)
(D) (0,6)

Correct Answer: C

Explanation:

Let the point be (0,y). Equating distances gives 9+(y−4)² = 25+(y−2)², hence y = 5.

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Question (16)

QN0036786

If P(x,y) is equidistant from A(7,1) and B(3,5), then the relation between x and y is

(A) x+y=2
(B) x−y=2
(C) x+y=4
(D) x−y=4

Correct Answer: B

Explanation:

Equating squared distances and simplifying gives x − y = 2.

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Question (17)

QN0036787

The midpoint of the line segment joining A(−4,6) and B(8,−2) is

(A) (2,2)
(B) (4,2)
(C) (2,4)
(D) (6,2)

Correct Answer: A

Explanation:

Midpoint = ((−4+8)/2, (6−2)/2) = (2,2).

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Question (18)

QN0036788

The midpoint of A(3,−5) and B(−7,9) is

(A) (−2,2)
(B) (2,−2)
(C) (−2,−2)
(D) (5,2)

Correct Answer: A

Explanation:

Midpoint = ((3−7)/2, (−5+9)/2) = (−2,2).

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Question (19)

QN0036789

The point dividing A(1,2) and B(11,7) internally in the ratio 3:2 is

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

Correct Answer: B

Explanation:

P = ((3×11+2×1)/5, (3×7+2×2)/5) = (7,5).

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Question (20)

QN0036790

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

(A) (−1,5/2)
(B) (1,−5/2)
(C) (−2,3)
(D) (2,−1)

Correct Answer: A

Explanation:

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

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Question (11)

The points A(0,0), B(6,0), and C(6,8) form a

Explanation:

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Question (12)

The points A(2,1), B(6,4), and C(10,7) are

Explanation:

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Question (13)

The point P(x,4) is equidistant from A(2,1) and B(6,1). The value of x is

Explanation:

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Question (14)

A point P(x,y) is equidistant from A(2,3) and B(6,7). Which relation is satisfied by x,y?

Explanation:

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Question (15)

The point on the y-axis equidistant from A(3,4) and B(−5,2) is

Explanation:

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Question (16)

If P(x,y) is equidistant from A(7,1) and B(3,5), then the relation between x and y is

Explanation:

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Question (17)

The midpoint of the line segment joining A(−4,6) and B(8,−2) is

Explanation:

Link:

Question (18)

The midpoint of A(3,−5) and B(−7,9) is

Explanation:

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Question (19)

The point dividing A(1,2) and B(11,7) internally in the ratio 3:2 is

Explanation:

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Question (20)

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

Explanation:

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