Question

For what value of 'y' the distance between the two points (2, y) and (10, -9) will be 10 units​

Answer 1

Answer:

-15 , -3

Step-by-step explanation:

Given,

A = (2 , y)

B = (10 , - 9)

Distance between the points is '10 units'

To Find :-

Value of 'y'

How To Do :-

As they given the value of the distance between the two points we need to equate that value to formula of distance between the two points and we need to substitute the values of the co-ordinates in the formula to get the value of 'y'.

Formula Required :-

Distance Formula :-

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

Solution :-

A = (2 , y)

Let ,

x_1 = 2 , y_1 = y

B = (10 , - 9)

Let ,

x_2 = 10 , y_2 = - 9

Distance(d) = 10

Substituting the values in the formula :-

$10=\sqrt{(10-2)^2+(-9-y)^2}$

$10=\sqrt{(8)^2+(-(9+y))^2}$

$10=\sqrt{64+(9+y)^2}$

$10=\sqrt{64+(9)^2+2(9)(y)+y^2}$

$10=\sqrt{64+81+18y+y^2}$

$10=\sqrt{145+18y+y^2}$

Squaring on both sides :-

$(10)^2=(\sqrt{145+18y+y^2})^2$

100 = 145 + 18y + y^2

y^2 + 18y + 145 - 100 = 0

y^2 + 18y + 45 = 0

y^2 + 15y + 3y + 45 = 0

Taking common :-

y(y + 15y) + 3(y + 15) = 0

(y + 15) (y + 3) = 0

Equating both the terms to '0' :-

y + 15 = 0 , y + 3 = 0

y = - 15 . y = - 3

∴ Value of 'y' = - 15 , - 3