Question

10 numeric 1 point a trapezoid is shown below. 32 72° (2x - 5) (5y - 2) 13 what must be the value of x? 11 fill in the blank 1 point quadrilateral abcd is an isosceles trapezoid. the coordinates for three of the vertices are given below. a (1,2), b (9,2), c (7,5) the coordinates for point d would be ( )

Explanation:

Step1: Apply the mid - segment formula of a trapezoid

The formula for the mid - segment \(m\) of a trapezoid is \(m=\frac{b_1 + b_2}{2}\), where \(b_1\) and \(b_2\) are the lengths of the two parallel sides. Here, \(b_1 = 32\), \(b_2=13\), and \(m = 2x - 5\).
So, \(2x-5=\frac{32 + 13}{2}\)

Step2: Simplify the right - hand side of the equation

First, calculate \(\frac{32+13}{2}=\frac{45}{2}=22.5\). Then the equation becomes \(2x-5 = 22.5\)

Step3: Solve for \(x\)

Add \(5\) to both sides of the equation: \(2x=22.5 + 5=27.5\). Then divide both sides by \(2\): \(x=\frac{27.5}{2}=13.75\)

Answer:

\(13.75\)