Question

write the coordinates of a point on x-axis which is equidistant from the points (-3,4) and (2,5)

Answer 1

Answer:

$\text{Point on x-axis is }(\frac{2}{5},0)$

Step-by-step explanation:

Given two coordinate points (-3,4) and (2,5). we have to find the point on x-axis which is equidistant from these two points.

Let the point be (a,0) the ordinate is taken to be 0 as the point lies on x-axis.

Using distance formula,

$Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Now, point (a,0) is  is equidistant from the points (-3,4) and (2,5)

$\sqrt{(-3-a)^2+(4-0)^2}=\sqrt{(2-a)^2+(5-0)^2}\\\\(-3-a)^2+16=(2-a)^2+25\\\\9+a^2+6a+16=4+a^2-4a+25\\\\10a=4\\\\a=\frac{4}{10}=\frac{2}{5}$

Hence, $\text{point on x-axis is }(\frac{2}{5},0)$