Question

graph a right triangle with the two points forming the hypotenuse. using the sides, find the distance between the two points, to the nearest tenth (if necessary).

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

click twice to draw a line. click a segment to erase it.

Explanation:

Step1: Identify the coordinates

Let the two points be \( (x_1, y_1) = (3, -6) \) and \( (x_2, y_2) = (6, 3) \).

Step2: Calculate the differences in coordinates

The horizontal difference (run) is \( \Delta x = x_2 - x_1 = 6 - 3 = 3 \).
The vertical difference (rise) is \( \Delta y = y_2 - y_1 = 3 - (-6) = 9 \).

Step3: Apply the distance formula

The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( d = \sqrt{(\Delta x)^2 + (\Delta y)^2} \).
Substituting the values, we get \( d = \sqrt{3^2 + 9^2} = \sqrt{9 + 81} = \sqrt{90} \).

Step4: Simplify and round

\( \sqrt{90} \approx 9.5 \) (to the nearest tenth).

Answer:

The distance between the two points is approximately \( 9.5 \).