Question

marco is writing a coordinate proof involving a right isosceles triangle. marco places his triangle on the coordinate plane such that the base of the triangle lies along the x - axis. what coordinates should he assign to this third vertex of the isosceles triangle? (2a, 2b) (b, a) (b, b) (a, b)

Explanation:

Step1: Find the x - coordinate of the third vertex

In an isosceles triangle with base along the x - axis from \((0,0)\) to \((2a,0)\), the x - coordinate of the vertex (the point opposite the base) is the mid - point of the base.
The mid - point formula for two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(x=\frac{x_1 + x_2}{2}\). Here \(x_1 = 0\) and \(x_2=2a\), so \(x=\frac{0 + 2a}{2}=a\).

Step2: Determine the y - coordinate of the third vertex

From the graph, the y - coordinate of the vertex is given as \(b\).

Answer:

\((a,b)\)