A line segment is a portion of a line with a measurable length. The midpoint of a line segment is the point exactly halfway between the endpoints. The midpoint bisects (cuts in half) the line segment.

You can only add or subtract monomials that have the same variable and the same exponent. For example, 2a + 4a = 6a and 4a² - a² = 3a² but 2a + 4b and 7a - 3b cannot be combined. However, you can multiply and divide monomials with unlike terms. For example, 2a x 6b = 12ab.

You need to find the value of c so solve the first equation in terms of y:

-7c + y = -1
y = -1 + 7c

then substitute the result (-1 - -7c) into the second equation:

-3c - 2(-1 + 7c) = -9
-3c + (-2 x -1) + (-2 x 7c) = -9
-3c + 2 - 14c = -9
-3c - 14c = -9 - 2
-17c = -11
c = \( \frac{-11}{-17} \)
c = \(\frac{11}{17}\)

To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:

a = s²

so the length of one side of the square is:

s = \( \sqrt{a} \) = \( \sqrt{64} \) = 8

The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:

c² = a² + b²
c² = 8² + 8²
c² = 128
c = \( \sqrt{128} \) = \( \sqrt{64 x 2} \) = \( \sqrt{64} \) \( \sqrt{2} \)
c = 8\( \sqrt{2} \)

A trapezoid is a quadrilateral with one set of parallel sides.