Question

(2, 5), (9, -7) and (9, 5)
step 2 of 2: what is the area of the triangle? (hint: make use of the mid - point formula if the triangle is isosceles.)
answer

Explanation:

Step1: Identify base and height

Let the points be \(A(2,5)\), \(B(9, - 7)\), \(C(9,5)\). The \(x -\)coordinates of \(B\) and \(C\) are the same (\(x = 9\)). The length of the vertical side (height \(h\)) between \(y=-7\) and \(y = 5\) is \(h=\vert5-(-7)\vert=12\). The length of the horizontal side (base \(b\)) between \(x = 2\) and \(x=9\) is \(b=\vert9 - 2\vert=7\).

Step2: Use area formula for triangle

The area formula for a triangle is \(A=\frac{1}{2}bh\). Substitute \(b = 7\) and \(h=12\) into the formula: \(A=\frac{1}{2}\times7\times12\).
\[A=\frac{7\times12}{2}=42\]

Answer:

42