Question

Two vertices of a right triangle are (0,1) and (0,6). The area of the triangle is 10 square units. Which point could be the third vertex of the triangle?

Answer 1

let's consider (0,1) and (0,6) to be the base,
the the base is 5 units.
let the height be h
giving us a nice isosceles triangle

(1/2)(5)h = 10
5h = 20
h = 4

so a possible third point is (4, 3.5)

As a matter of fact, we could now take any point along the vertical line x = 4
Since x = 4 is parallel to the y-axis, the distance between them is always 4 and the base of our triangle is always 5, giving us an area of
(1/2)(4)(5) = 10

A third point looks like (4, k), where k is any real number.

Answer 2

Forgot to mention that we could also have placed out third point on the left side of the y-axis,
e.g. (-4,8) would work