Question

(iv) Which point on X-axis is equidistant from the points A (-3, 4) and B (7,6)?​

Answer 1

Step-by-step explanation:

Let the co-ordinates of the required point on x-axis be P (x, 0). The given points are A (7, 6) and B (-3, 4). Thus, the required point is (3, 0).

Answer 2

On x-axis, y = 0 therefore let point P(x, 0) be equidistant from A and B.

As P is equivalent from A and B, AP = BP

AP = √[(x + 3)² + (y - 4)²]

BP = √[(x - 7)² + (y - 6)² ]

As AP = BP, we can equate them and solve for 'x'

√[(x + 3)² + (0 - 4)²] = √[(x - 7)² + (0 - 6)² [ y = 0 ]

squaring both sides, we get

(x + 3)² + (0 - 4)² = (x - 7)² + (0 - 6)²

=> x² + 6x + 9 + 16 = x² - 14x + 49 + 36

=> 6x + 25 = 85 - 14x

[ distance formula d = √[(x2 - x1)² + (y2 - y1)² ]

=> 6x + 14x = 85 - 25

=> 20x = 60

=> x = 3

the point equidistant from A and B is P (3, 0)