Question

The coordinates of the endpoints of ST are (-2,3) and (3, y) respectively supposethe distance between s and t us 13 units.What values of life would satisfy the given condition?Justify your answer

Answer 1

The values of y would be -9 and 15

Explanation:

we know that

the formula to calculate the distance between two points is equal to

`d=\sqrt{(y2-y1)^(2)+(x2-x1)^(2)}`

we have

`d=13\ units`

S(-2,3) and T(3,y)

substitute the given values in the formula and solve for y

`13=\sqrt{(y-3)^(2)+(3+2)^(2)}`

`13=\sqrt{(y-3)^(2)+25}`

squared both sides

`169=(y-3)^(2)+25`

`(y-3)^(2)=169-25`

`(y-3)^(2)=144`

take square root both sides

`y-3=(+/-)12`

`y=3(+/-)12`

`y=3(+)12=15`

`y=3(-)12=-9`

therefore

The values of y would be -9 and 15