Question

finding the area of a right triangle with legs not parallel to the coordinate axes
triangle abc is a right triangle
the length of bc is 5 units.
the area of abc is square units.

Explanation:

Step1: Calculate the length of \(AB\)

Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). For points \(A(-9,10)\) and \(B(7,-2)\), we have \(x_1=-9,y_1 = 10,x_2=7,y_2=-2\).

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Step2: Calculate the area of the right - triangle

The area formula for a right - triangle is \(A=\frac{1}{2}\times base\times height\). Here, if \(BC = 5\) (height) and \(AB\) (base) \(=20\).

$$A=\frac{1}{2}\times AB\times BC=\frac{1}{2}\times20\times5$$

Answer:

\(50\)