Question

directions: find the coordinates of the midpoint of the segment given its endpoints

1. a(5, 8) and b(-1, -4)
2. m(-5, 9) and n(-2, 7)
3. p(-3, -7) and q(3, -5)
4. f(2, -6) and g(-8, 5)

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$.

Step2: Solve for problem 6

For points $A(5,8)$ and $B(-1,-4)$, $x_1 = 5$, $y_1 = 8$, $x_2=-1$, $y_2=-4$. Then $x=\frac{5+( - 1)}{2}=\frac{4}{2}=2$ and $y=\frac{8+( - 4)}{2}=\frac{4}{2}=2$. The mid - point is $(2,2)$.

Step3: Solve for problem 7

For points $M(-5,9)$ and $N(-2,7)$, $x_1=-5$, $y_1 = 9$, $x_2=-2$, $y_2 = 7$. Then $x=\frac{-5+( - 2)}{2}=\frac{-7}{2}=-3.5$ and $y=\frac{9 + 7}{2}=\frac{16}{2}=8$. The mid - point is $(-3.5,8)$.

Step4: Solve for problem 8

For points $P(-3,-7)$ and $Q(3,-5)$, $x_1=-3$, $y_1=-7$, $x_2 = 3$, $y_2=-5$. Then $x=\frac{-3 + 3}{2}=0$ and $y=\frac{-7+( - 5)}{2}=\frac{-12}{2}=-6$. The mid - point is $(0,-6)$.

Step5: Solve for problem 9

For points $F(2,-6)$ and $G(-8,5)$, $x_1 = 2$, $y_1=-6$, $x_2=-8$, $y_2 = 5$. Then $x=\frac{2+( - 8)}{2}=\frac{-6}{2}=-3$ and $y=\frac{-6 + 5}{2}=-\frac{1}{2}=-0.5$. The mid - point is $(-3,-0.5)$.

Answer:

1. $(2,2)$
2. $(-3.5,8)$
3. $(0,-6)$
4. $(-3,-0.5)$