Question

2 vertices of a triangle are 1,-4 and 6,-4. List 2 possible coordinates of the third vertex so that the triangle has an area of 20 units.

Answer 1

Let the line joining (1,-4) and (6,-4) be the base of your triangle.
This is a horizontal line, and it should be easy to see that its length is 5
let the height be h
(1/2)(5)h = 20
5h = 40
h = 4
so any point on the x-axis (or 4 units above your base) would be such a third point
possible cases:
(5,0) and (8,0)
you could also have points along a line 4 units below your base, or a y value of -8
two such points are:
(3,-8) and (7, -8)

Answer 2

how do you do this on a coordnate plane.

Answer 3

Just to clarify I think the first one is wrong 5x 4= 20 and it has to be 20 but triangles you divide by 1/2 and it'd be ten