Question

question 2
right triangle abc is on a coordinate plane segment ab is on the line ( y = 2 ) and is 5 units long. point c is on the line ( x = - 2 ). if the area of ( \triangle abc ) is 12.5 square units, then find a possible y - coordinate of point c

Explanation:

Step1: Use the area formula for a right - triangle

The area formula for a right - triangle is \(A=\frac{1}{2}\times base\times height\). Here, let \(AB\) be the base. Given \(AB = 5\) units and \(A=12.5\) square units.

Step2: Solve for the height

Substitute the values into the formula \(12.5=\frac{1}{2}\times5\times h\).
First, simplify the right - hand side: \(\frac{1}{2}\times5\times h=\frac{5h}{2}\).
Then, solve the equation \(12.5=\frac{5h}{2}\) for \(h\). Multiply both sides by \(2\): \(12.5\times2 = 5h\), so \(25 = 5h\). Divide both sides by \(5\): \(h = 5\).

Step3: Find the \(y\) - coordinate of point \(C\)

Since \(AB\) is on the line \(y = 2\) and the height \(h\) is the vertical distance from \(AB\) to point \(C\). If the height \(h = 5\), then \(y=2 + 5=7\) or \(y=2-5=-3\) (but since \(7\) is one of the options)

Answer:

\(7\)