NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 7: Coordinate Geometry
Exercise 7.1

Coordinate Geometry MCQs: distance formula, section formula, rectangles/triangles, perpendicular bisectors.

Question.  1

The distance of the point \(P(2,3)\) from the x-axis is

(A)

2

(B)

3

(C)

1

(D)

5

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Question.  2

The distance between the points \(A(0,6)\) and \(B(0,-2)\) is

(A)

6

(B)

8

(C)

4

(D)

2

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Question.  3

The distance of the point \(P(-6,8)\) from the origin is

(A)

8

(B)

\(2\sqrt{7}\)

(C)

10

(D)

6

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Question.  4

The distance between the points \((0,5)\) and \((-5,0)\) is

(A)

5

(B)

\(5\sqrt{2}\)

(C)

\(2\sqrt{5}\)

(D)

10

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Question.  5

AOBC is a rectangle whose three vertices are \(A(0,3),\ O(0,0)\) and \(B(5,0)\). The length of its diagonal is

(A)

5

(B)

3

(C)

\(\sqrt{34}\)

(D)

4

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Question.  6

The perimeter of a triangle with vertices \((0,4),(0,0),(3,0)\) is

(A)

5

(B)

12

(C)

11

(D)

\(7+\sqrt{5}\)

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Question.  7

The area of a triangle with vertices \(A(3,0),\ B(7,0)\) and \(C(8,4)\) is

(A)

14

(B)

28

(C)

8

(D)

6

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Question.  8

The points \((-4,0),(4,0)\) and \((0,3)\) are the vertices of a

(A)

right triangle

(B)

isosceles triangle

(C)

equilateral triangle

(D)

scalene triangle

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Question.  9

The point which divides the line segment joining \((7,-6)\) and \((3,4)\) in ratio \(1:2\) internally lies in the

(A)

I quadrant

(B)

II quadrant

(C)

III quadrant

(D)

IV quadrant

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Question.  10

The point which lies on the perpendicular bisector of the line segment joining the points \(A(-2,-5)\) and \(B(2,5)\) is

(A)

(0, 0)

(B)

(0, 2)

(C)

(2, 0)

(D)

(-2, 0)

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Question.  11

The fourth vertex \(D\) of a parallelogram \(ABCD\) whose three vertices are \(A(-2,3),\ B(6,7)\) and \(C(8,3)\) is

(A)

(0, 1)

(B)

(0, -1)

(C)

(-1, 0)

(D)

(1, 0)

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Question.  12

If the point \(P(2,1)\) lies on the line segment joining points \(A(4,2)\) and \(B(8,4)\), then

(A)

\(AP=\dfrac{1}{3}\,AB\)

(B)

\(AP=PB\)

(C)

\(PB=\dfrac{1}{3}\,AB\)

(D)

\(AP=\dfrac{1}{2}\,AB\)

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Question.  13

If \(P\big(\dfrac{a}{3},4\big)\) is the mid-point of the line segment joining the points \(Q(-6,5)\) and \(R(-2,3)\), then the value of \(a\) is

(A)

-4

(B)

-12

(C)

12

(D)

-6

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Question.  14

The perpendicular bisector of the line segment joining the points \(A(1,5)\) and \(B(4,6)\) cuts the y-axis at

(A)

(0, 13)

(B)

(0, -13)

(C)

(0, 12)

(D)

(13, 0)

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Question.  15

The coordinates of the point which is equidistant from the three vertices of \(\triangle AOB\) as shown in Fig. 7.1 is

Fig. 7.1

(A)

(x, y)

(B)

(y, x)

(C)

\(\big(\dfrac{x}{2},\dfrac{y}{2}\big)\)

(D)

\(\big(\dfrac{y}{2},\dfrac{x}{2}\big)\)

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Question.  16

A circle drawn with origin as the centre passes through \(\big(\dfrac{13}{2},0\big)\). The point which does not lie in the interior of the circle is

(A)

\(\big(-\dfrac{3}{4},1\big)\)

(B)

\(\big(2,\dfrac{7}{3}\big)\)

(C)

\(\big(5,-\dfrac{1}{2}\big)\)

(D)

\(\big(-6,\dfrac{5}{2}\big)\)

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Question.  17

A line intersects the y-axis and x-axis at the points \(P\) and \(Q\), respectively. If \((2,-5)\) is the mid-point of \(PQ\), then the coordinates of \(P\) and \(Q\) are, respectively

(A)

(0, -5) and (2, 0)

(B)

(0, 10) and (-4, 0)

(C)

(0, 4) and (-10, 0)

(D)

(0, -10) and (4, 0)

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Question.  18

The area of a triangle with vertices \((a,b+c)\), \((b,c+a)\) and \((c,a+b)\) is

(A)

\((a+b+c)^2\)

(B)

0

(C)

\(a+b+c\)

(D)

\(abc\)

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Question.  19

If the distance between the points \((4,p)\) and \((1,0)\) is 5, then the value of \(p\) is

(A)

4 only

(B)

\(\pm 4\)

(C)

-4 only

(D)

0

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Question.  20

If the points \(A(1,2)\), \(O(0,0)\) and \(C(a,b)\) are collinear, then

(A)

\(a=b\)

(B)

\(a=2b\)

(C)

\(2a=b\)

(D)

\(a=-b\)

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NCERT Exemplar Solutions Class 10 – Mathematics – CHAPTER 7: Coordinate Geometry – Exercise 7.1 | Detailed Answers