Ques 1 The point on X-axis which is equidistant from the points (2, -2) and (-4,2) is(a) (1,0) (b) (2,0) (c) (0,2) (d) (-1,0)

Let's solve this step by step:

Step 1: We know that any point on the x-axis has the form (x, 0).

Step 2: We need to find the point (x, 0) that is equidistant from the points (2, -2) and (-4, 2). This means that the distance from (x, 0) to (2, -2) is equal to the distance from (x, 0) to (-4, 2).

Step 3: We can use the distance formula to set up the equation. The distance formula is √[(x2-x1)² + (y2-y1)²].

Step 4: Setting up the equation, we get:

√[(x-2)² + (0-(-2))²] = √[(x-(-4))² + (0-2)²]

Step 5: Squaring both sides to get rid of the square root, we get:

(x-2)² + 4 = (x+4)² + 4

Step 6: Simplifying, we get:

x² - 4x + 4 + 4 = x² + 8x + 16 + 4

Step 7: Subtracting x² from both sides and simplifying, we get:

-4x + 8 = 8x + 20

Step 8: Solving for x, we get:

x = -1

So, the point on the x-axis that is equidistant from the points (2, -2) and (-4, 2) is (-1, 0). Therefore, the correct answer is (d) (-1,0).