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

Answer:

The values of y would be -9 and 15

Step-by-step 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