Calculate the midpoint of the segment with the given endpoints. $G(5,3), H(-5,-3)$

Ascertain whether the quadrilateral $A B C D$ is a parallelogram, rhombus, square, rectangle, or none of these. List each that applies. Explain.

$$A(1,3), B(7,-3), C(1,-9), D(-5,-3)$$

A parallelogram has vertices $A(0,2), B(2,-1), C(6,3)$, and $D(p, q)$. Which of the following ordered pairs has possible values for $(p, q)$ ? A. $(0,6)$ B. $(6,1)$ C. $(4,6)$ D. $(6,4)$

Given that the augmented matrix in row reduced form is equivalent to the augmented matrix of a system of linear equations, (a) determine whether the system has a solution and (b) find the solution or solutions to the system, if they exist.

$$\left[\begin{array}{lll|l} 1 & 0 & 0 & 2 \\ 0 & 0 & 0 & 1 \end{array}\right]$$

Calculate the midpoint of the segment with the given endpoints. $I(6,-1), J(-2,5)$

convert 100 yards to feet (1 yard = 3 feet). Round the result to the nearest tenth

Find (a) the distance between P and Q and (b) the coordinates of the midpoint M of the segment joining P and Q.

$$P(-6,-10), Q(6,5)$$

Find (a) the distance between P and Q and (b) the coordinates of the midpoint M of the segment joining P and Q.

$$P(-7,4), Q(6,-2)$$

The coordinates of the vertices of parallelogram PQRS are given. Decide whether PQRS is best described as a rhombus, a rectangle, or a square. Explain your reasoning. $P(-1,2), Q(2,5), R(5,2), S(2,-1)$

Evaluate the integral by making a suitable change of variables.

$$\iint\limits_R (2x+y)\ dA$$

where R is the parallelogram bounded by the lines x+y=-1, x+y=3, 2x-y=0, and 2x-y=4.

Place a check next to each sentence in which the subject and verb agree. _____ Some people is experimenting with ostrich farms.

If a pair of opposite sides of $A B C D$ are parallel and congruent, then it is a parallelogram. (Hint: Let $\overline{A B} \| \overline{D C}$, $\overline{A B} \cong \overline{D C}$ and draw $\overline{B D}$.) (Use congruence geometry.)

Use the method described in the earlier example to rewrite the rational expression, sketch the graph by hand, and generate an accurate depiction of each function with a graphing calculator:

$$f(x)=\frac{-2 x-5}{x+3}$$

Find the midpoint of the line segment whose endpoints are $(-2, 5)$ and $(4, -9)$.