Question

In the following exercise-$(-3,-3)and(6,-1)$

(a) find the midpoint of the line segments whose endpoints are given and,

(b) plot the endpoints and the

midpoint on a rectangular coordinate system.

Short answer

(a) The mid point of the given points is $(\frac{3}{2},-2)$.

(b) Plotting the points on the coordinate system gives us,

Step-by-step solution

Step 1. Given and explanation.

We have the points as $(-3,-3),(6,-1)$.

We will use the formula for calculating mid point of two given points, i.e., $(x_1,y_1),(x_2,y_2)$. Formula is-

Midpoint=$(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$.
Plotting all the three points give us the graph.

Step 2. Finding the mid point.

Consider $(-3,-3)$as $(x_1,y_1)$and $(6,-1)$as $(x_2,y_2)$.

Substituting the values in the formula gives us,
Midpoint=$(\frac{-3+6}{2},\frac{-3+(-1)}{2})$
$$\begin{gathered} =(\frac{3}{2},\frac{-4}{2}) \\ =(\frac{3}{2},-2) \end{gathered}$$
Thus we get this as the mid point.

Step 3. Sketching the line.

Plotting all the three points on the rectangular coordinate plane gives us,