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:

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

Where $(x_1,y_1)=(9,1)$ and $(x_2,y_2)=(-3,6)$.

Calculating the distance:

$$d=\sqrt{((-3)-9{)}^2+(6-1{)}^2}$$ $$d=\sqrt{(-12{)}^2+(5{)}^2}$$ $$d=\sqrt{144+25}$$ $$d=\sqrt{169}$$ $$d=13$$

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

Question 2: Finding the midpoint

To find the midpoint of the segment connecting the two points, we can use the midpoint formula:

$$M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$$

Using the points $(9,1)$ and $(-3,6)$:

$$M=(\frac{9+(-3)}{2},\frac{1+6}{2})$$ $$M=(\frac{6}{2},\frac{7}{2})$$ $$M=(3,3.5)$$

Thus, the midpoint of the segment is $(3,3.5)$.