Question

find the coordinates of a point equidistant from the point Q (5,4) and R ( -2 , 3)​

Answer 1

Answer:

9 ,1 is the answer coordinates

Answer 2

Given :

Q = (5 , 4)

R = (-2 , 3)

To find :

The coordinates of a point equidistant from the point Q (5 , 4) and R (-2 , 3).

Solution :

​As we know the Mid point is equidistant from the two points which are given.

So, to find the coordinate of such a point, we can find the Mid point.

$Mid-point = (\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )$

$Mid-point = (\frac{5+(-2)}{2} ,\frac{4+3}{2} )$

$Mid-point = (\frac{3}{2} ,\frac{7}{2} )$

Mid-point = (1.5 , 3.5)

Therefore, the coordinates are (1.5 , 3.5)

Verification :

To check whether the coordinates are correct or not, find the distance between the mid-point and Q and R.

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

Distance between the mid-point and Q

$D1 = \sqrt{(1.5-5)^{2} + (3.5-4)^{2} }$

$D1 = \sqrt{(-3.5)^{2} +(-0.5)^{2} }$

$D1 = \sqrt{12.25 + 0.25 }$

$D1 = \sqrt{12.5}$

Distance between the mid-point and R

$D2 = \sqrt{(1.5-(-2))^{2} +(3.5-3)^{2} }$

$D2 = \sqrt{(3.5)^{2} + (0.5)^{2} }$

$D2 = \sqrt{12.25 + 0.25 }$

$D2 = \sqrt{12.5}$

D1 = D2 = $\sqrt{12.5}$

Hence verified.