Question

Find the distance between the pair of points. Round to the nearest tenth.

(-4, 0) and ( 6, -8)

Question 16 options:

8.2


12.8


7.7


4.2

Question 17 (1 point)
Find the midpoint of the line segment with the given endpoints.

(0, 6) and (-3, -3)

Question 17 options:

(-6, -12)


(1.5, 4.5)


(-1.5, 1.5)


(3, -3)

Question 18 (2 points)
A student solved the following problem. State if the answer is correct.

Find the other endpoint of the line segment with the given endpoint and midpoint.

Endpoint: (−4, 0), midpoint: (8, 3)

Answer: (20, 6)

Question 18 options:
True
False

Answer 1

**Question 16:** To find the distance between the points \((-4, 0)\) and \((6, -8)\), we use the distance formula:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Substituting in the values:

- \(x_1 = -4\)
- \(y_1 = 0\)
- \(x_2 = 6\)
- \(y_2 = -8\)

\[
d = \sqrt{(6 - (-4))^2 + (-8 - 0)^2}
\]

This simplifies to:

\[
d = \sqrt{(6 + 4)^2 + (-8)^2}
\]
\[
d = \sqrt{10^2 + (-8)^2}
\]
\[
d = \sqrt{100 + 64}
\]
\[
d = \sqrt{164}
\]

Calculating the square root:

\[
d \approx 12.81
\]

Rounding to the nearest tenth, the distance is **12.8**.

**Question 17:** To find the midpoint of the line segment with endpoints \((0, 6)\) and \((-3, -3)\), we use the midpoint formula:

\[
M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)
\]

Substituting in the values:

- \(x_1 = 0\)
- \(y_1 = 6\)
- \(x_2 = -3\)
- \(y_2 = -3\)

Calculating the coordinates of the midpoint:

\[
M = \left(\frac{0 + (-3)}{2}, \frac{6 + (-3)}{2}\right)
\]

This simplifies to:

\[
M = \left(\frac{-3}{2}, \frac{3}{2}\right) = \left(-1.5, 1.5\right)
\]

So the midpoint is **(-1.5, 1.5)**.

**Question 18:** To find the other endpoint given one endpoint \((-4, 0)\) and the midpoint \((8, 3)\), we use the formula for the midpoint:

If \(M\) is the midpoint and \(A\) is one endpoint, then the other endpoint \(B\) can be found using:

\[
M = \left(\frac{x_A + x_B}{2}, \frac{y_A + y_B}{2}\right)
\]

Solving for \(B\):

\[
M_x = \frac{x_A + x_B}{2} \quad \Rightarrow \quad 8 = \frac{-4 + x_B}{2} \quad \Rightarrow \quad 16 = -4 + x_B \quad \Rightarrow \quad x_B = 20
\]

\[
M_y = \frac{y_A + y_B}{2} \quad \Rightarrow \quad 3 = \frac{0 + y_B}{2} \quad \Rightarrow \quad 6 = y_B
\]

Thus, the other endpoint is \((20, 6)\). Therefore, the student's answer is **True**, it is correct.

### Final Answers:
- **Question 16:** 12.8
- **Question 17:** (-1.5, 1.5)
- **Question 18:** True