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

Accepted Solution

Answer:The values of y would be -9 and 15Step-by-step explanation:we know thatthe formula to calculate the distance between two points is equal to [tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex] we have[tex]d=13\ units[/tex]S(-2,3) and T(3,y)substitute the given values in the formula and solve for y[tex]13=\sqrt{(y-3)^{2}+(3+2)^{2}}[/tex] [tex]13=\sqrt{(y-3)^{2}+25}[/tex] squared both sides[tex]169=(y-3)^{2}+25[/tex] [tex](y-3)^{2}=169-25[/tex] [tex](y-3)^{2}=144[/tex] take square root both sides[tex]y-3=(+/-)12[/tex][tex]y=3(+/-)12[/tex][tex]y=3(+)12=15[/tex][tex]y=3(-)12=-9[/tex]thereforeThe values of y would be -9 and 15