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

O 7.2 units
• 13.0 units
• 14.2 units
• 8.0 units
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 \((x_2, y_2) = (-3, 6)\).

Substituting the values into the formula:

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

Thus, 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:

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

Substituting the coordinates:

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

Therefore, the midpoint of the segment is (3, 3.5).