Angles around a line add up to 180°. Angles around a point add up to 360°. When two lines intersect, adjacent angles are supplementary (they add up to 180°) and angles across from either other are vertical (they're equal).

The area of a trapezoid is one-half the sum of the lengths of the parallel sides multiplied by the height:

a = ½(b + d)(h)
a = ½(4 + 5)(5)
a = ½(9)(5)
a = ½(45) = \( \frac{45}{2} \)
a = 22\(\frac{1}{2}\)

You need to find the value of b so solve the first equation in terms of z:

-7b + z = 2
z = 2 + 7b

then substitute the result (2 - -7b) into the second equation:

-b - 7(2 + 7b) = 2
-b + (-7 x 2) + (-7 x 7b) = 2
-b - 14 - 49b = 2
-b - 49b = 2 + 14
-50b = 16
b = \( \frac{16}{-50} \)
b = -\(\frac{8}{25}\)

The slope of this line is the change in y divided by the change in x. The endpoints of this line segment are at (-2, 2) and (2, -10) so the slope becomes:

According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:

c² = a² + b²
c² = 9² + 6²
c² = 81 + 36
c² = 117
c = \( \sqrt{117} \)