Question

Two of the vertices of a triangle (0,1) and (4,1). Which coordinates of the third vertex make the area of the triangle equal 16

Answer 1

Answer:

If triangle is a right triangle, then four possible solutions exist: 1) (0, 10), 2) (0, - 8), 3) (4, 10), 4) (4, - 8)

Step-by-step explanation:

Let suppose that figure is a right triangle. Geometrically speaking, the area of the triangle is represented by the following formula:

$A = \frac{1}{2}\cdot b\cdot h$ (1)

Where:

$b$ - Base.

$h$ - Height.

$A$ - Area of the triangle.

Besides, let consider that line segment is between (0, 1) and (4, 1). The length of the base is determined by Pythagorean Theorem:

$b = \sqrt{(4-0)^{2}+(1-1)^{2}}$

$b = 4$

If we know that $A = 16$ and $b = 4$, then the height of the triangle is:

$h = \frac{2\cdot A}{b}$

$h = 9$

There are four possible solutions for the coordinates of the vertex of the triangle:

1) (0, 10), 2) (0, - 8), 3) (4, 10), 4) (4, - 8)