Question

multiple choice 1 point
what are the coordinates of the mid - point of the segment with endpoints at (-3, -4) and (5, 8)?
(1, 2)
(2, 4)
(4, 6)
(8, 12)
multiple choice 1 point
∠p and ∠q are supplementary. m∠p = 5x + 3 and m∠q = x + 3. x = _?

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Here $x_1=-3,y_1 = - 4,x_2 = 5,y_2=8$.

Step2: Calculate x - coordinate of mid - point

$x=\frac{-3 + 5}{2}=\frac{2}{2}=1$.

Step3: Calculate y - coordinate of mid - point

$y=\frac{-4 + 8}{2}=\frac{4}{2}=2$.
So the mid - point of the segment is $(1,2)$.

Step4: Recall supplementary angles property

If $\angle P$ and $\angle Q$ are supplementary, then $m\angle P+m\angle Q = 180^{\circ}$.

Step5: Set up the equation

We have $(5x + 3)+(x + 3)=180$.

Step6: Simplify the left - hand side

$5x+3+x + 3=6x+6$.

Step7: Solve the equation

$6x+6 = 180$. Subtract 6 from both sides: $6x=180 - 6=174$. Then divide both sides by 6: $x=\frac{174}{6}=29$.

Answer:

1. A. (1, 2)
2. C. 29