Important Questions: Coordinate Geometry - Class 10 MCQ

To find the value of x, we can use the distance formula, which states that the distance between two points (x₁, y₁) and (x₂, y₂) is given by:

D = √((x₂ - x₁)² + (y₂ - y₁)²)

In this case, the points are (2, -2) and (-1, x). The distance is given as 5. Therefore, we have:

5 = √((-1 - 2)² + (x + 2)²)

Squaring both sides gives:

25 = (3)² + (x + 2)²

25 = 9 + (x + 2)²

Subtracting 9 from both sides:

16 = (x + 2)²

Taking the square root of both sides:

±4 = x + 2

This gives us two equations:

• x + 2 = 4 → x = 2
• x + 2 = -4 → x = -6

Thus, one of the values of x is 2. Therefore, the correct answer is option B.

Explanation of Incorrect Options

• A. -2: This value does not satisfy the distance equation derived above.
• C. -1: This value does not satisfy the distance equation derived above.
• D. 1: This value does not satisfy the distance equation derived above.

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

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

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

Isosceles triangle.

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

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

Diagonals of parallelogram bisect each other.