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

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:

(1)

Where:

- Base.

- Height.

- 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:

If we know that and , then the height of the triangle is:

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)

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step-by-step explanation:

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