Question

If the ends of the base of an isosceles triangle are at (2,0) & (0,1) & the eqn of one side is
x=2,
then the orthocentre of the triangle is

a) (3/2, 3/2)
b) (5/4, 1)
c) (3/4, 1)
d) (4/3, 7/12)

Answer 1

What are your ideas?

Answer 2

Well nothing !

Answer 3

Where do you feel the third point would lie?

Answer 4

Try plotting the 2 points on paper and also the line x=2

Answer 5

Sorry I don't have any idea as I have never touched this topic :(

Answer 6

Ok
Can you plot the two points on a piece of paper after drawing the co-ordinate axis?

Answer 7

Ok but it will take some time !

Answer 8

See, you have one equation give to you.This mean that 2 points of the triangle will lie on that equation,which is x=2.

Answer 9

with me so far?

Answer 10

right

If you say i will upload the pic. of the graph

Answer 11

yaaaaaa

Answer 12

So have you managed to locate the third point on the graph?

Answer 13

just a second i m drawing the graph

Answer 14

you have one point (0,1) on th y-axis.and one point (2,0) on the x-axis.Right?

Answer 15

right

Answer 16

now, you also have the equation x=2. That is a line parallel to the y-axis but passing through (2,0)

Answer 17

Here is the graph

Answer 18

now the third point lies on x=2 as well.So what do you think the thrid point is, such that its an isoceles triangle?

Answer 19

sry i think the graph is wrong

Answer 20

How will i draw its graph !!!!!!!!

Answer 21

I have an idea can we use the distance formula

Answer 22

so how do you plan to do it? find the distance between (0,1) and (2,0).
Now the third point should be on the line x=2, so the point will be of the form (2,a)
so find the distance between (0,1) and (2,a).This should be equal to the distance between (0,1 and 2,0)

Answer 23

Hi guys, before going on... x=2 is a vertical line which takes on all y-values for x=2

Answer 24

So now the third point be (2,2)

Answer 25

b)(5,4,1)

Answer 26

5/4,1

Answer 27

There may be another way to do it, but I centered a circle at (0,1) and another at (2,0) and set their radii equal (isosceles triangle). The orthocenter is the intersection of the altitudes.