Question

I need help finding the intersection point of the altitudes and the sides of a triangle?

Answer 1

i think thats called the orthocenter

Answer 2

No, I don't need to find the orthocenter yet. I need to know the coordinates of the point where the altitude and one of the sides of the triangle meet

Answer 3

well, if you have the vertex, you can find the equation of line that pass through the vertex and find teh intersection with the equation of altitude

Answer 4

you can find the intersect by solving a linear system of equations

Answer 5

hint: the line from the vertex will have a slope = -1/slope of the line AC

Answer 6

Oh, find the equation that passes through the vertex, get the slope of the perpendicular line that passes through the opposite vertex and find the intersection

Answer 7

Okay, I'll see if I can do that

Answer 8

What is the equation to finding a perpendicular line?

Answer 9

once you have the slope of a line, m, then perpendicular line will have slope -1/m

Answer 10

find the equation of AC then find the equation of the altitude using -1/slope of AC an the point B

Answer 11

now that u have the slope, u know that the perpendicular line must pass through the opposite vertex. You have slope and point, now find the equation

Answer 12

then solve the 2 lines simultaneously

Answer 13

and find the intersection point

Answer 14

Oh okay! I think I know how to do it now, thank you!

Answer 15

Np :)

Answer 16

An altitude is a line segment from a vertex to the opposite side and perpendicular to it.

To find the equation of an altitude

i). find the slope of the side opposite the vertex from which the altitude is produced. The negative reciprocal of this slope is then the slope of the altitude,

ii). Using the slope of the altitude from i) and the vertex point, find the equation of the line.

iii). repeat steps i) and ii) to find the equation of the altitude from a different vertex.

iv). by the method of substitution or elimination find the point of intersection of the two altitudes. This point of intersection is the orthocenter.

Answer 17

Thank you very much! :)

Answer 18

Welcome! I hope that helps.

Answer 19

Good Luck!