Question

c. you can graph the segments to find the point where they intersect. do the segments intersect at one of the midpoints? explain your reasoning. a(-3, 2) b(5, 2) c(1, 1) d(1, 7)

Explanation:

Step1: Find mid - point of segment AB

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. For $A(-3,2)$ and $B(5,2)$, we have $x=\frac{-3 + 5}{2}=1$ and $y=\frac{2+2}{2}=2$, so the mid - point of $AB$ is $(1,2)$.

Step2: Find mid - point of segment CD

For $C(1,1)$ and $D(1,7)$, $x=\frac{1 + 1}{2}=1$ and $y=\frac{1+7}{2}=4$, so the mid - point of $CD$ is $(1,4)$.

Step3: Analyze intersection

By looking at the graph, we can see that the intersection point of segments $AB$ and $CD$ is $(1,2)$ which is the mid - point of segment $AB$.

Answer:

Yes, the segments intersect at the mid - point of segment $AB$ which is $(1,2)$.