Important Questions: Coordinate Geometry - Class 10 MCQ

# Important Questions: Coordinate Geometry - Class 10 MCQ

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## 10 Questions MCQ Test Mathematics (Maths) Class 10 - Important Questions: Coordinate Geometry

Important Questions: Coordinate Geometry for Class 10 2024 is part of Mathematics (Maths) Class 10 preparation. The Important Questions: Coordinate Geometry questions and answers have been prepared according to the Class 10 exam syllabus.The Important Questions: Coordinate Geometry MCQs are made for Class 10 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Important Questions: Coordinate Geometry below.
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Important Questions: Coordinate Geometry - Question 1

### If the distance between the points (2, - 2) and (-1, x) is 5, one of the values of x is

Detailed Solution for Important Questions: Coordinate Geometry - Question 1

Let us consider the points as

A = (2, -2)

B = (-1, x)

AB = 5 units

Using the distance formula

AB2 = (x₂ - x₁)2 + (y₂ - y₁)2

Substituting the values

52 = (-1 - 2)2 + (x + 2)2

25 = (-3)2 + (x + 2)2

Using the algebraic identity

(a + b)2 = a2 + b2 + 2ab

25 = 9 + x2 + 4 + 4x

By further calculation

25 = x2 + 4x + 13

x2 + 4x + 13 - 25 = 0

x2 + 4x - 12 = 0

By splitting the middle term

x2 + 6x - 2x - 12 = 0

Taking out the common terms

x(x + 6) - 2(x + 6) = 0

(x + 6)(x - 2) = 0

So we get

x + 6 = 0

x = -6

And

x - 2 = 0

x = 2

Important Questions: Coordinate Geometry - Question 2

### A triangle with vertices (4, 0), (- 1, - 1) and (3, 5) is a/an

Detailed Solution for Important Questions: Coordinate Geometry - Question 2

Let A(4, 0), B(-1, -1), C(3, 5)

⇒ AB2 + AC2 = BC2 and AB = AC
Hence, triangle is an isosceles right-angled triangle.

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Important Questions: Coordinate Geometry - Question 3

### The points A (9, 0), B (9, 6), C (-9, 6) and D (-9, 0) are the vertices of a

Detailed Solution for Important Questions: Coordinate Geometry - Question 3

AB= √(9-9)²+(6-0)²=6
BC= √(-9-9)²+(6-6)²=18
CD = √(-9+9)²+(0-6)²=6
DA = √(-9-9)²+(0-0)²=18
so,it's opposite sides are equal,hence it is rectangle

Important Questions: Coordinate Geometry - Question 4

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

Detailed Solution for Important Questions: Coordinate Geometry - Question 4

Isosceles triangle.

Important Questions: Coordinate Geometry - Question 5

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

Detailed Solution for Important Questions: Coordinate Geometry - Question 5

Since both these points lie on a straight line i.e x axis, distance will be the difference between the respective y coordinates
(0,-2) & (0,6)  =>  6-(-2)) = 6+2 = 8

Important Questions: Coordinate Geometry - Question 6

A circle drawn with origin as the centre passes through  The point which does not lie in the interior of the circle is

Detailed Solution for Important Questions: Coordinate Geometry - Question 6

Distance of  from centre of the circle i. e.

Important Questions: Coordinate Geometry - Question 7

The distance between the points A (0, 7) and B (0, -3) is

Detailed Solution for Important Questions: Coordinate Geometry - Question 7

Since both these points lie on a straight line i.e x axis, distance will be the difference between the respective y coordinates

(0,-3)   (0,7)

7-(-3) = 7+3 = 10

Important Questions: Coordinate Geometry - Question 8

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

Detailed Solution for Important Questions: Coordinate Geometry - Question 8

Important Questions: Coordinate Geometry - Question 9

The end points of diameter of circle are (2, 4) and (-3, -1). The radius of the circle is

Detailed Solution for Important Questions: Coordinate Geometry - Question 9

Important Questions: Coordinate Geometry - Question 10

If P(1, 2), Q(4,6), R(5,7) and S(a, b) are the vertices of a parallelogram PQRS, then

Detailed Solution for Important Questions: Coordinate Geometry - Question 10

Diagonals of parallelogram bisect each other.

## Mathematics (Maths) Class 10

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## Mathematics (Maths) Class 10

116 videos|420 docs|77 tests