Question

I really need help with this please.

Answer 1

y = - 6x + 7.5

Explanation:

the perpendicular bisector of BC passes through the midpoint of BC at right angles to BC.

calculate the slope m of BC using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = B (- 2, 1 ) and (x₂, y₂ ) = C (4, 2 )

`m_(BC)` =
`(2-1)/(4-(-2))` =
`(1)/(4+2)` =
`(1)/(6)`

given a line with slope m then the slope of a line perpendicular to it is

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/((1)/(6) )` = - 6

the midpoint of BC is the average of the x and y coordinates

midpoint = (
`(-2+4)/(2)` ,
`(1+2)/(2)` ) = (
`(2)/(2)` ,
`(3)/(2)` ) = ( 1, 1.5 )

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - 6 , then

y = - 6x + c ← is the partial equation

to find c substitute (1, 1.5 ) into the partial equation

1.5 = - 6 + c ⇒ c = 1.5 + 6 = 7.5

y = - 6x + 7.5 ← equation of perpendicular bisector of BC