Question

Given triangle GHI with G(4.-3), H(-4,2), and I(2,4), find the perpendicular bisector of line HI in standard form.

I really need help on this.....I'm totally confused.

Answer 1

first find the slope of the of the line HI, you can use the point-slope formula to do this:
\[y_2-y_1 = m*(x_2-x_1)\]
lets rename m to m_a

once you found the slope, m_a, for the line HI, find the slope of a line that would be perpendicular to it. the perpendicular slope we will call m_b. use the equation for perpendicular slopes:
\[m_a * m_b = -1\]
plug in m_a, and solve the equation for m_b. you now have the slope of the line that is perpendicular to the line HI.

Take m_b, and point 'G'. plug those values into the standard slope-intercept form equation of
y = mx+b
solve for b.

once you have 'b' re write the equation of y=mx+b, but only plug in the value for 'm' and the value for 'b'

Answer 2

Oh my gosh! thank you so much!

Answer 3

Hold on.. I'm stuck on the last part. When i first write y=mx+b what do I plug in where??

Answer 4

y=mx+b
for x and y, plug in the point G, so (4, -3)
for m, plug in what you solved for as the slope of the perpendicular line slope

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Answer 5

aha, thank you!!

Answer 6

:D

Answer 7

...I got y=-1 1/3x+7/3 haha, did i go wrong somewhere?

Answer 8

ya, there was a little mix up somewhere,

so the slope of the HI line is
m = 1/3 or
m_a = 1/3
then
m_b = -3

do you see where u slipped up?

Answer 9

Yeah! i got mixed up in the second equation... Ok, i got it now, y=-3x+9??

Answer 10

excellent work,
so right now
y=-3x+9 is in slope intercept form
so re write the equattion into standard form
Ax + By = C

Answer 11

Whoa, what.

Answer 12

haha, so just rearrange the equation
y=-3x+9
so that 9 is by itself

Answer 13

i'm logging off,
hope you got it figured out!

Answer 14

thank you (: I got it.