What is the Orthocenter of Y(3,-2) A(3,5) B(9,1)

Answer 1

the orthocenter is the intersection of the three altitudes

draw a diagram on graph paper

line AB has equation y=(-2/3)x+7 (you should know how to find this equation and all the others))

the altitude from Y to this line is y=(3/2)x-(13/2)

line YB has equation y=(1/2)x-(7/2)

the altitude from A to this line is y=-2x+11

this is all you need to know to find the orthocenter

you could have used any two sides and their altitudes

where these lines intersect is the orthocenter

use the two altitudes

y=(3/2)x-(13/2)

y=-2x+11

solve this system of equations

-2x+11=(3/2)x-(13/2)

(13/2)+11=(3/2)x+2x

(13/2)+(22/2)=(3/2)x+(4/2)x

35/2=(7/2)x (you should see that x=5; if not see the next step)

x=(35/2)(2/7)

x=5

substitute into either equation to get the y-value

y=-2(5)+11

y=-10+11

y=1

the orthocenter is (5,1)