1. ## Triangle ABC...

Triangle ABC is isosceles with BC=AC. The coordinates of the vertices are A(6, 1) and B(2, 8).
Find the equation of the perpendicular bisector of AB.
If the x coordinate of C is 3.5, find the y coordinate of C.
Find the length of AB.
Find the area of triangle ABC.

2. a)
1. Find the gradient of AB.
3. Find the midpoint of AB
4. Use the point from 3. and the gradient fom 2. to get the perpendicular bisector of AB.

b)
1. Since this is an isosceles triangle, AC = BC. Use the distance formula:

$\displaystyle AC = BC$

$\displaystyle AC^2 = (x_a - x_c)^2 + (y_a - y_c)^2$

$\displaystyle BC^2 = (x_b - x_c)^2 + (y_b - y_c)^2$

$\displaystyle (x_a, y_a) = (6, 1)\ , \ (x_b, y_b) = (2, 8)\ and \ (x_c, y_c) = (3.5, y_c)$

c)
Use the distance formula again.

$\displaystyle AB^2 = (x_a - x_b)^2 + (y_a - y_b)^2$

d)
1. You have the midpoint AB, label it X. Find the distance XC.

2. Now, use $\displaystyle Area\ of\ triangle = \dfrac12 \times base \times height$

Where base = AB, height = XC

3. Thanks so much. That mostly makes perfect sense.
But I don't completely understand what I'm meant to do for part b.
Do you think you could try to help me through it??

4. As I told you AB = BC, hence;

$\displaystyle AB^2 = BC^2$

Replace by what I told you, and you get:

$\displaystyle (x_a - x_c)^2 + (y_a - y_c)^2 = (x_b - x_c)^2 + (y_b - y_c)^2$

Substitute the values you know, to find the value of yc

5. Originally Posted by mandarep
Thanks so much. That mostly makes perfect sense.
But I don't completely understand what I'm meant to do for part b.
Do you think you could try to help me through it??
TRY and show what you are able to do yourself.

For this particular problem you don't really need to find those slopes. For an isosceles triangle, the perpendicular bisector of the base passes through the vertex angle. The perpendicular bisector of AB is the line through the midpoint of AB and C.

6. Hello mandarp,
I believe the best way to solve problems like these is to plot and do as much as possible without writing equations.In this particular case you would find out that the x value for C could be in error because it is very close to the midpoint of AB

bjh

7. Hi guys.
Thanks so much for trying to help me out.
I ended up working through it, by substituting the values in.
Sorry I just couldn't realise what to do before. Thanks again for everyone's help.