Question

Consider a triangle with vertices A(1,8), B(3,2) and C(7,0).
(a) Find the equation of a straight line L1 that is perpendicular to AC and the point of intersection of L1 and AC lies on the line y=x.
(b) Find the equation of a straight line L2 that is parallel to AC and passes through the circumcenter of triangle ABC.

Answer 1

I will teach you if you're willing to learn. If you're simply looking for someone to give you the answers and the solutions, then tell me now because I won't do that.

Answer 2

I am not looking for the answers, I just want to learn how to do this type of question

Answer 3

I think my way is not the clever one.

For part a) Find the equation of a straight line L1 that is perpendicular to AC // and the point of intersection of L1 and AC lies on the line y=x.

1. find the equation of AC. Then, find the slope of AC. Then slope of L1 = 1/ slope of AC
2. Find the intersection point of AC and the line y=x.
3. You have a point, and a slope of L1, you can find the equation of L1.

Answer 4

For part b) Find the equation of a straight line L2 that is parallel to AC //and passes through the circumcenter of triangle ABC.

1. you have a slope of AC (from part a) Since AC//L2, they have the same slope
2. Find the circumcentre of the triangle (By distance formula?!)
3. Find the equation you need with the slope and the point (coord. of the circumcentre)

Answer 5

@Callisto

Clever lol :D

Answer 6

@Callisto. Guess u meant to say
the slope of L1=-1/slope of AC:)

Answer 7

thank you @Callisto :)

Answer 8

@ajprincess Yes! Yes! Sorry!!! Sorry!!!
1. find the equation of AC. Then, find the slope of AC. Then slope of L1 = -1/ slope of AC

@kryton1212 You're welcome~

Answer 9

That's ok. great work @callisto:)

Answer 10

Nice effort @Callisto