SOLUTION: Hello.. I need to find the orthocenter of a triangle with coordinates: G(-2,5) H(6,5) J(4,-1) AND... A(4,-3) B(8,5) C(8,-8) Thanks to whoever answers this question!!!

Question 174559This question is from textbook
: Hello..
I need to find the orthocenter of a triangle with coordinates:
G(-2,5)
H(6,5)
J(4,-1)
AND...
A(4,-3)
B(8,5)
C(8,-8)
Thanks to whoever answers this question!!! This question is from textbook

Answer by jojo14344(1513) (Show Source): You can put this solution on YOUR website!

Let's draw the triangle with following vertices:
G(-2,5)
H(6,5)
J(4,-1)

Now, we draw a line from the vertex that is perpendicular to the opposite side.
1) from point G (-2,5) thru line HJ with points (6,5) & (4,-1):

, Slope
Since perpendicular,--->
Then, via Slope-Intercept Form, on point G:
--->

Therefore, the line eqn -----> , Line passing thru point G perpendicular to Line HJ
2) from point H (6,5) thru line GJ with points (-2,5) & (4,-1):

, Slope
Also, ---->
Then, via point (6,5):
---->
Therefore,
, Line passing thru point H perpendicular to Line GJ
.
3)from point J (4,-1) thru Line GH with points (-2,5) & (6,5):
We can see Line GH has no Slope, only horizontal line (y=5), so line perpendicular to it from point (4,-1) is , vertical line,slope is
.
Plug in "highlighted" in the graph:
---------->
Graph on the LEFT, See LINES from one vertex perpendicular to the other side.
Graph on the RIGHT, Lines intersect at one point --->(4,3), orthocenter, ANSWER.
.
NEXT
Let's draw the Triangle with following vertices:
Points
A(4,-3)
B(8,5)
C(8,-8)

The same we did the last one,drawing a Line from the vertex that is perpendicular to the opposite side:
1)As you can see on point A (4,-3) is going thru vertical LINE BC and the line from point (4,-3) should be perpendicular to BC---->
.
2)Point B (8,5) thru Line AC with points (4,-3) & (8,-8):
}

And, , perpendicular right?

Then,thru point (8,5): via Slope-Intercept Form
--->

So, it follows ------->
.
3)Point C (8,-8) thru line AB with points (4,-3) & (8,5):

Then,
Thru point (8,-8):
----->

It follows------>
.
Plug in "highlighted" in the graph;
------>
-------> Orthocenter lies outside the Triangle, being "Obtuse Triangle" >>>> point (-2,-3), ANSWER
Thank you,
Jojo

RELATED QUESTIONS
Find the coordinates of the centroid, orthocenter, and circumcenter of a triangle with... (answered by solver91311,richard1234)
a b c d e f g h i j k l m n o p q r (answered by ewatrrr)
please help. i need answers. i have school tommorow and i need these by tommorow.pleasee. (answered by solver91311)
The endpoints of GH are G(6,-12) and H(-4,-8). What are the coordinates of the midpoint... (answered by thesvw)
Determine whether the given coordinates are the vertices of a triangle. 1. A(3,5),... (answered by richwmiller,Edwin McCravy)
(answered by ewatrrr)
Let U = {a, b, c, d, e, f, g, h, i, j, k, l, m, n}, L = {a, b, c, d, e, f, g} and S = {a, (answered by Edwin McCravy)
puhlezz help,..were given this assignment. How to graph a coordinate plane?? the quetion (answered by jim_thompson5910)
I NEED HELP. PLEASE HELP ME ASAP. THANKS BEFORE :) 1) The straight line with equation... (answered by richard1234)