Question

Please help me to solve the question. ​

Answer 1

Answer:
`y=(9)/(2)x+(51)/(4)` → y = 4.5x + 12.75

Explanation:

Perpendicular Bisector means the line goes through the midpoint and has the opposite reciprocal slope.

Use the Midpoint formula:
`M=\bigg((x_1+x_2)/(2),(y_1+y_2)/(2)\bigg)`

`M=\bigg((-6+3)/(2),(7+5)/(2)\bigg)\\\\\\.\ =\bigg((-3)/(2),(12)/(2)\bigg)\\\\\\.\ =\bigg(-(3)/(2),6\bigg)`

Use the Slope formula:
`m=(y_2-y_1)/(x_2-x_1)`

`m=(7-5)/(-6-3)\quad =\quad (2)/(-9)\quad =\quad -(2)/(9)`

Perpendicular slope is opposite (change the sign) and reciprocal (flip the fraction).
`m_(\perp)=+(9)/(2)`

Now use the Point-Slope formula: y - y₁ = m⊥ (x - x₁) where

• (x₁, y₁) is the midpoint (-3/2, 6)
• m⊥ = 9/2

`y-6=(9)/(2)\bigg(x+(3)/(2)\bigg)\\\\\\y-6=(9)/(2)x+(27)/(4)\\\\\\y\quad =(9)/(2)x+(27)/(4)+(24)/(4)\\\\\\.\quad \large\boxed{y =(9)/(2)x+(51)/(4)}`