A right triangle in the coordinate plane has vertices at (1,c), (1,–3), and (–2,–3). If c is a positive number and the area of the triangle is 6 square units, what is the value of c?c=
Question
A right triangle in the coordinate plane has vertices at (1,c), (1,–3), and (–2,–3). If c is a positive number and the area of the triangle is 6 square units, what is the value of c?c=
Solution
The area of a triangle is given by the formula 1/2 * base * height.
In this case, the base of the triangle is the distance between the points (1, -3) and (-2, -3), which is 3 units.
The height of the triangle is the distance between the points (1, c) and (1, -3), which is |c - (-3)| = |c + 3| units.
Given that the area of the triangle is 6 square units, we can set up the equation:
1/2 * base * height = area 1/2 * 3 * |c + 3| = 6 |c + 3| = 4
Since c is a positive number, we can discard the negative solution and solve for c:
c + 3 = 4 c = 4 - 3 c = 1
So, the value of c is 1.
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