Question

Please help me bef9yer9h

Answer 1

The answer is y = -6x + 15/2.

First, find the slope of BC.

m = Δy/Δx

m = 2 - 1 / 4 - (-2)

m = 1/6

Hence, the slope of the perpendicular bisector will be the negative reciprocal of the given line.

m' = - (1/ [1/6])

m' = -6

Now, find the midpoint of BC.

M = (-2 + 4 / 2, 2 + 1 / 2)

M = (1, 3/2)

Now, we can find the equation of the perpendicular bisector using the point slope form of equation.

y - y₁ = m (x - x₁)

y - 3/2 = -6 (x - 1)

y - 3/2 = -6x + 6

y = -6x + 15/2

Answer 2

y = -6x + 7.5

Step-by-step explanation:

To find perpendicular bisector equation:

Given points: B(-2, 1), C(4, 2)

First find slope:

`\sf slope: (y_2 - y_1)/(x_2- x_1) \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points`

`\sf slope: (2-1)/(4-(-2)) } = (1)/(6)`

Then the perpendicular slope will be negatively inverse.

`\sf perpendicular \ slope \ (m) : -((1)/(6) )^(-1) = -6`

Then find the mid point coordinates between BC:

`(x_m, y_m)= \sf ((x_1 + x_2)/(2) , (y_2 + y_1)/(2) )`

`(x_m, y_m) = \sf ((-2 + 4)/(2) , (1 + 2)/(2) )`

`(x_m, y_m) = \sf ( 1 , 1.5 )`

Then find equation:

y - yₘ = m(x - xₘ)

y - 1.5 = -6(x - 1)

y = -6x + 6 + 1.5

y = -6x + 7.5