Answer:
t= 11
Step-by-step explanation:
[tex]\boxed{gradient = \frac{y1 - y2}{x1 - x2} }[/tex]
Gradient of line that contains points (3, 7) & (5, 11)
[tex] = \frac{11 - 7}{5 - 3} [/tex]
[tex] = \frac{4}{2} [/tex]
= 2
The product of the gradients of two perpendicular lines is -1.
Gradient of the line that contains points (t, -2) & (-3, 5)
= -1 ÷2
[tex] = - \frac{1}{2} [/tex]
[tex] \frac{ - 2 - 5}{t - ( -3 )} = - \frac{1}{2} [/tex]
[tex] \frac{ - 7}{t + 3} = \frac{ - 1}{2} [/tex]
Cross multiply:
-(t +3)= -7(2)
Dividing by -1 on both sides:
t +3= 7(2)
t +3= 14
t= 14 -3
t= 11
