Question

find the value of y ,if the distance between the points (2,y) and (-4,5) is 10

Answer 1

Answer:

$\large\star\:\large\boxed{\:\:y=13,\:(-3)\:\:}\:\large\star$

Step-by-step explanation:

★Given:-

The distance between (2,y) and (-4,5) is 10.

★To Find:-

The Value of y.

★Formula Used:-

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

★Solution:-

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ ,where x₁=2, x₂=(-4), y₁=y and y₂=5.

$\implies10=\sqrt{[(-4)-2]^2+(5-y)^2}$

$\implies10=\sqrt{(-6)^2+(5-y)^2}$

Squaring both Sides:-

$\implies(10)^2=(\sqrt{(-6)^2+(5-y)^2})^2$

$\implies100={(-6)^2+(5-y)^2}$

$\implies100=36+25+y^2-10y$

$\implies y^2-10y-100+61=0$

$\implies y^2-10y-39=0$

$\implies y^2-13y+3y-39=0$

$\implies y(y-13)+3(y-13)=0$

$\implies (y+3)(y-13)=0$

$\implies y=13,\:(-3)$

Answer 2

Hi,your answer is 13 and -3.

Hope this helps you a lot..