Question

A line segment with endpoints A = (3, 0) and B = (7,0). Then, plot all points

C = (x, y) such that the triangle ABC has an area of 12 square units.
What geometric formula and theorem are needed to solve this problem?

Answer 1

C(0,6)

Explanation:

1) find the length of the base of the triangle

AB = 7-3 = 4

2) find the the height of the triangle

A = (base x height)/2

A x 2 = base x height

height = (A x 2)/base

height = (12 x 2)/4 = 6

3) find the equation of the line that passes threw the points AB

the two points have the same y so the equation of the line is

y = 0

4) use the formula of the distance between a point and a line to find C

|ax+by+c|/√a^2 + b^2 = distance

x = 0

y = 6

C (0,6)