Question

Consider triangle ABC with vertices A(4,8), B(0,0) and C(6,0). AQ and BP are two altitudes of triangle ABC. AQ and BP meet at H.
(a) Find the equations of AQ and BP.
(b) Find the coordinates of H.
(c) If CR is the third altitude of ABC, show that CR also passes through H.

Answer 1

could you draw a corresponding figure ?

Answer 2

to get the equation of AQ, u need its slope,
to get its slope u need slope of BC, which is ?

Answer 3

can u find slope of BC ?

Answer 4

or, did u realize that AQ is a vertical line ?

Answer 5

yes

Answer 6

slope of BC=6 ?

Answer 7

no, slope of BC = (0-0)/(6-0) = 0
right ? u know slope formula ?

Answer 8

oh I forgot that the line which is horizontal and the slope is zero.
ok...

Answer 9

right, and vertical line's equation is of the form ?

Answer 10

vertical line.....slope is undefined right?

Answer 11

yup,. the equation of vertical line is of the form x=c
c is the x-co-ordinate.

Answer 12

got it.

Answer 13

got the equation of both the lines ?

Answer 14

AQ=4 ---> x=4

BP=1/4
y=(1/4)x+0
y=(1/4)x

Answer 15

yup, now u know how to find co-ordinates of H ?

Answer 16

wait a minute, let me write that down...

Answer 17

H(4,1)

Answer 18

yup.

Answer 19

got it

Answer 20

can u find equation of CR in same way ?

Answer 21

let me think.........

Answer 22

find slope of AB first.....

Answer 23

finding....
mAB=8-0/4-0=2

Answer 24

slope of CR * slope of AB=-1
mCR= -1 / 2

Answer 25

yep, now equation of CR

Answer 26

I cannot get the equation...............

Answer 27

y-y1 = m(x-x1)
m =-1/2
x1,y1 = 6,0

Answer 28

oh I need to substitute the coordinates of H into the formula, right?

Answer 29

not H,
put co-ordinates of C

Answer 30

got it.

Answer 31

because u need to prove that H lies on CR, so u can't use H

Answer 32

oh yes, I find it just now....thank you :)

Answer 33

good, welcome ^_^