Question

I WILL GIVE MEDAL
Given triangle ABC with A(-4, -2), B(4, 4), and C(18, -8), Write the equation of the line containing the altitude that passes through B in standard form.

Answer 1

please help

Answer 2

anyone

Answer 3

i think for this you'd have to use the distance formula

Answer 4

how would i set that up

Answer 5

still very confused

Answer 6

can you explain more?

Answer 7

So since the altitude is perpendicular to the opposing side, we have have to find the equation of AC.

Answer 8

how do i do that

Answer 9

im sorry im very tired

Answer 10

that's fine same here

Answer 11

let's see:
\[m = \frac{ -8 - (-2) }{ 18 - (-4) } = \frac{ -6 }{ 22 } = \frac{ -3 }{ 11 }\]
But since we're looking for the perpendicular slope, we find the inverse reciprocal:
\[\frac{ -3 }{ 11 } \rightarrow \frac{ 11 }{ 3 }\]
this is our slope for the altitude.
\[y = f(4) = 4 = \frac{ 11 }{ 3 } (4) + b\]
now, we just have to pass through point B (4,4). So to get it in standard form:
\[y-4 = \frac{ 11 }{ 3 }(x-4)\]
\[y - 4 = (\frac{ 11 }{ 3 })x - \frac{ 44 }{ 3 }\]
\[(\frac{ -11 }{ 3 })x + y = 4 - \frac{ 44 }{ 3 }\]
\[\frac{ -11 }{ 3 }x + y = \frac{ -32 }{ 3 }\]
and there you have it.

But please double check my work just in case.

Answer 12

thank you so much

Answer 13

You're welcome