Question

I WILL GIVE MEDAL
ABC has vertices A(0, 6), B(4, 6), and C(1, 3). Sketch a graph of ABC and use it to find the orthocenter, including any necessary points or slopes you had to derive.
(PLEASE PLEASE PLEASE help i need help fast)

Answer 1

JaziLove
Do you know how to graph it?

Answer 2

Not really

Answer 3

Well, i think so,, but i dont know what to do after that

Answer 4

The point where the three altitudes of a triangle intersect. The altitude of a triangle (in the sense it used here) is a line which passes through a vertex of the triangle and is perpendicular to the opposite side. There are therefore three altitudes possible, one from each vertex

Circumcentre Definition: Located at intersection of the perpendicular bisectors of the sides. The circumcenter is also the center of the triangle's circumcircle - the circle that passes through all three of the triangle's vertices.

Incentre Definition: Located at intersection of the angle bisectors. The incenter is the center of the triangle's incircle, the largest circle that will fit inside the triangle and touch all three sides

Try drawing these triangles on graph paper. You will see these three centres.

Answer 5

I'm still confused on how to work the problem

Answer 6

@pooja195 please help

Answer 7

anyone please help

Answer 8

I'm still here - just finishing up a graphic

Answer 9

oh ok

Answer 10

hello

Answer 11

@wolf1728

Answer 12

Okay, I'm back. I had to redraw the graphic to include the "6"

Answer 13

In the graph the "x" axis has numbers that go left to right
the "y" axis has numbers that go from bottom to top

Answer 14

how would i solve it step by step

Answer 15

So, to plot point A, you would need to put a point at x=0 and y=6
I just put it into the graphic

Answer 16

I just plotted the points for B and C and put those in the graphic

Answer 17

ok

Answer 18

is there more?

Answer 19

Yes because now you have to calculate where the orthocenter is
(wow this problem requires a lot doesn't it?)

Answer 20

yes it does *sigh*

Answer 21

how do i fond the orthocenter

Answer 22

I just drew a few lines to make a triangle of the 3 points.
I think I might do a quick web search to see about "orthocenter"

Answer 23

alright

Answer 24

GEEZ - here's a site that tells how to do it:
https://www.easycalculation.com/analytical/orthocenter-triangle.php
Seems you have to find the slopes of the lines
(Guess I'll read some more)

Answer 25

whoa, this is a very difficult problem, thank you for helping for this long

Answer 26

Okay I'll keep going if you want

Answer 27

please

Answer 28

Sure

Answer 29

Slope of line AB =0
Slope of line AC = (6-3)/(0-1) = 3/-1 = -3
Slope of line CB = (3-6) / (1-4) = -3/-3 = 1
Now it looks as if we move on to Step 2 on the orthocenter page

Answer 30

looks like itxD

Answer 31

Slope of AD= 1/(slope BC) = 1/1 = 1
slope of BE = 1/(slope AC) = (1/-3)
slope of CF = 1/(slope AB) = (1/0) = Infinite

Answer 32

im kind of confused about the last part

Answer 33

Heck, I have found this exact problem worked out here:
https://www.wyzant.com/resources/answers/2717/abc_has_vertices_a_0_6_b_4_6_and_c_1_3_find_the_orthocenter_of_abc_list_your_steps
Incidntally, the anwer turns out to be (1,5)
or x=1 y=5
which is right where I drew it !!

Answer 34

wow haha thanks for everything

Answer 35

Okay you are welcome
I really didn't show you all the equations to get the answer but I think that site shows you how to do it.
Here's my final graphic with the orthocenter drawn in!

Answer 36

Thanks for the medal :-)