Lulu marks the points (9,1) and (-3,6) on a coordinate plane. What is the distance between these two points, rounded to the nearest tenth of a unit?(1 point)

Question

Responses

8.0 units
8.0 units

7.2 units
7.2 units

13.0 units
13.0 units

14.2 units
14.2 units
Question 2
What is the midpoint of the segment? If not a whole number, write as a decimal(1 point)
(
,
)

Answer 1

To find the distance between the points \( (9,1) \) and \( (-3,6) \), we can use the distance formula:

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

Here, \( (x_1, y_1) = (9, 1) \) and \( (x_2, y_2) = (-3, 6) \).

Plugging in the values:

\[ d = \sqrt{((-3) - 9)^2 + (6 - 1)^2} \]

Calculating the differences:

\[ d = \sqrt{(-12)^2 + (5)^2} \] \[ d = \sqrt{144 + 25} \] \[ d = \sqrt{169} \] \[ d = 13 \]

So, the distance between the two points is 13.0 units.

---

Next, to find the midpoint of the segment connecting the points \( (9,1) \) and \( (-3,6) \), we use the midpoint formula:

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

Plugging in the coordinates:

\[ \text{Midpoint} = \left( \frac{9 + (-3)}{2}, \frac{1 + 6}{2} \right) \] \[ \text{Midpoint} = \left( \frac{6}{2}, \frac{7}{2} \right) \] \[ \text{Midpoint} = (3, 3.5) \]

So, the midpoint of the segment is \( (3, 3.5) \).

To summarize:

1. The distance is 13.0 units.
2. The midpoint is \( (3, 3.5) \).