ACT 1 Geo: Find distance and midpoint

$Q_{1}:$ If $M$ is the .....................of $\overline{PR}$ , then $PM=MR=\frac{1}{2}PR.$

$Q_{2}:$ Points $A, B, M$ and $C$ lie on the line as shown below. Point $M$ is the midpoint of $\overline{AC}$. If $BM=6$ and $AB=\frac{2}{3}MC$, what is the length of $AM$?

$Q_{3}:$ In the figure below, $Q$ is the midpoint of $PR$. If $PQ =x + 3$ and $QR =2x -1 $, what is the length of segment $PR $?

$Q_{4}:$ What is the formula of midpoint between two points?

$Q_{5}:$ The center of a circle is the .............. of its diameter.

$Q_{6}:$ Which of the following is the distance formula?

$Q_{7}:$ Use the distance formula to find the diameter of the circle at points $(-4,8),(2,-4).$.

$Q_{8}:$ Which of the following represents an equation of a circle whose diameter has endpoints $(-8,4)$ and $(2, -6)$?

$Q_{9}:$ The midpoint of the segment joining $(-4, 1)$ to $(-2,-9)$ is $

$Q_{10}:$ Let $ AB$ is the diameter of a circle whose center is $O$. If the coordinates of $A$ are $(2, 6)$ and the coordinates of $B$ are $(6, 2)$, find the coordinates of $O$.

$Q_{11}:$ Let $DC$ is the diameter of a circle whose center is $O$. If the coordinates of $O$ are $(2, 1)$ and the coordinates of $C$ are $(4, 6)$, find the coordinates of $D$.

$Q_{12}:$ Find the distance from the point whose coordinates are $(4, 3)$ to the point whose coordinates are $(8, 6).$

$Q_{13}:$ The vertices of a triangle are $(2, 1), (2, 5),$ and $(5, 1)$. The area of the triangle is

$Q_{14}:$ In isosceles triangle $RST$, $RS = ST$. If $A$ is the midpoint of $RS$ and $B$ is the midpoint of $ST$, then

$Q_{15}:$ What is the equation of the line connecting the midpoint of line segment $AB$ with point $C$ in the figure above?

$Q_{16}:$ Find the perimeter of $ABC$ given its vertices are $A(2, 2)$, $B(-1, 5)$, and $C(-5, 2)$.

$Q_{17}:$ Find the area of parallelogram $ABCD$ given its vertices are $A(3, 1)$, $B(2, -1)$, $C(-1, -1)$, and $D(0, 1)$.

$Q_{18}:$ If the distance from $A(1, 6)$ to $B(x, -2)$ is $10$, then what is a possible value for $x$?

$Q_{19}:$ If the distance from $D(x, 1)$ to $C(x, -2)$ is $x$, then what is a possible value for $x$?

$Q_{20}:$ A point $Q$ is in the second quadrant at a distance of from the origin. Which of the following could be the coordinates of $Q$?

$Q_{21}:$ If $M$ is the midpoint of $\overline{AB}$. Find the coordinates of $B$ if $A$ has coordinates $(3, 8)$ and $M$ has coordinates $(-4, 0)$.

$Q_{22}:$ Which of the following points is farthest from the point $(2, 2) $?

$Q_{23}:$ If $C(3, -4)$ and $D(7,2)$ are the endpoints of diameter $CD$ of circle $O$, what are the coordinates of $O$?

$Q_{24}:$ Eman is setting up flags for a relay race. The race’s starting line is one hundred meters north and one hundred meters east from the concession stand, and it will be run in a straight line to the finish line, located five hundred meters north of the concession stand and three hundred meters east of it. Eman has been instructed to set up flags halfway to the finish line. Where should she set up the flags relative to the concession stand?

$Q_{25}:$ The distance between points $P$ and $Q$ in the $(x, y)$ coordinate plane is half the distance between $(-4, 2)$ and $(-8, 1)$. What is the distance between points $P$ and $Q $?

$Q_{26}:$ In the following figure, the midpoint of line $MN$ is $P$, while the midpoint of the line segment $QP$ is $R$. If the length of $QR$ is $6$ and the length of $MQ$ is $4$, what is the length of $MN$?