Triangle WXY, with vertices W(2,-9), X(6,-8), and Y(5,-6), is drawn inside a rectangle.What is the area, in square units, of triangle WXY.

Answer 1

To find the area of the triangle WXY, we can use the formula for the area of a triangle given the coordinates of its vertices.

First, we need to find the base and height of the triangle. The base of the triangle is the distance between the points W(2,-9) and X(6,-8), which can be calculated using the distance formula:

Base = √((6-2)^2 + (-8+9)^2) = √(4^2 + 1) = √(16 + 1) = √17

Next, we need to find the height of the triangle. One way to do this is to draw a perpendicular line from point Y(5,-6) to the base WX. This perpendicular line will be the height of the triangle.

Since the line passes through point Y(5,-6) and is perpendicular to the base WX, the height of the triangle is the vertical distance between point Y and the line segment WX, which is |y-coordinate of Y - y-coordinate of W|.

Height = |-6 - (-9)| = 3

Now, we can use the formula for the area of a triangle:

Area = 0.5 * base * height
Area = 0.5 * √17 * 3
Area ≈ 2.598 square units

Therefore, the area of triangle WXY is approximately 2.598 square units.