find the equation of the straight line through A(3,20) which is perpendicular to the line passing through the points B(-2,8) and C(11,8). Hence, find the area of the triangle ABC, giving your answer in the simplest possible form.

Answer 1

slope of BC = (8-8)/(11=2) = 0
so BC is a horizontal line
Thus the line through A must be a vertical line
All vertical lines have the form x = something
Look at the given point A, what is its x value ?
so the equation of your required line is
x = 3

Make a sketch.
The base BC of the triangle is 13 units long, and A is 12 units above BC
so the base is 13 and the height is 12
Area = (1/2)(13)(12) = 78 units^2

Answer 2

Why is the base BC is 13, its because x2-x1? and why is 12 in A?

Answer 3

BC = 11 - (-2) = 13

what is the difference between a height of 8 and a height of 20 ??

Did you look at your diagram?

Answer 4

oh, okay. thank you very much for your help