Question

graph $\triangle wxy$ with vertices $w(2,3),x(-2,-2)$, and $y(-2,3)$. what is the area of $\triangle wxy$? area = square units

Explanation:

Step1: Identify base and height

The base of the triangle can be found by calculating the horizontal distance between \(W(2,3)\) and \(Y(- 2,3)\). The formula for the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) for points with the same \(y - \)coordinate is \(d=\vert x_1 - x_2\vert\). Here, \(x_1 = 2\), \(x_2=-2\), \(y_1 = y_2=3\), so the base \(b=\vert2-(-2)\vert = 4\). The height \(h\) of the triangle is the vertical distance between the line \(y = 3\) and the point \(X(-2,-2)\). Using the formula for the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) for points with the same \(x - \)coordinate (in this case we consider the vertical distance), \(h=\vert3-(-2)\vert=5\).

Step2: Apply triangle - area formula

The area formula for a triangle is \(A=\frac{1}{2}bh\). Substitute \(b = 4\) and \(h = 5\) into the formula. So \(A=\frac{1}{2}\times4\times5\).

Step3: Calculate the area

\(A=\frac{1}{2}\times4\times5=10\).

Answer:

10