Question

points a, b, c, and d on the figure below are collinear. use the figure for exercise 3.

1. if ac = 24, what is ab?

use the figure shown for exercises 4.

1. what is m∠ptr?
2. what is the midpoint formula?

for exercises 6, find the midpoint of each segment with the given endpoints.

1. a(-4, 6) and b(10, -10)

for exercise 7, find the other endpoint of the segment given the midpoint and one endpoint.

1. midpoint(-3, -8) and endpoint(-6.5, -4.5)

for exercise 8, find the coordinates of the point described in relation to line segment cd.

1. 1/3 of the way from c to d

Explanation:

Step1: Solve for Exercise 3

Given $AC = 24$, assume $AB=x$ and $BC = 4x - 13$. Since $AC=AB + BC$, we have $x+(4x - 13)=24$.
Combining like - terms gives $5x-13 = 24$.
Adding 13 to both sides: $5x=37$, so $x=\frac{37}{5}=7.4$.

Step2: Solve for Exercise 5

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

Step3: Solve for Exercise 6

Using the mid - point formula with $A(-4,6)$ and $B(10,-10)$.
$x=\frac{-4 + 10}{2}=\frac{6}{2}=3$, $y=\frac{6+( - 10)}{2}=\frac{-4}{2}=-2$. The mid - point is $(3,-2)$.

Step4: Solve for Exercise 7

Let the mid - point $M(-3,-8)$ and one endpoint $E(-6.5,-4.5)$. Let the other endpoint be $(x,y)$.
We have $\frac{-6.5 + x}{2}=-3$ and $\frac{-4.5 + y}{2}=-8$.
For $x$: $-6.5+x=-6$, so $x = 0.5$.
For $y$: $-4.5 + y=-16$, so $y=-11.5$. The other endpoint is $(0.5,-11.5)$.

Answer:

1. $AB = 7.4$
2. $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$
3. $(3,-2)$
4. $(0.5,-11.5)$