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, 7)\\) and \\((-5, 5)\\)\\(click twice to draw a line. click a segment to erase it.)

Explanation:

Step1: Identify the coordinates

Let the two points be \( (x_1, y_1) = (-3, 7) \) and \( (x_2, y_2) = (-5, 5) \).

Step2: Calculate the differences in coordinates

The horizontal difference (run) is \( \Delta x = x_2 - x_1 = -5 - (-3) = -2 \), and the vertical difference (rise) is \( \Delta y = y_2 - y_1 = 5 - 7 = -2 \).

Step3: Apply the distance formula

The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \). Substituting the values, we get \( d = \sqrt{(-2)^2 + (-2)^2} \).

Step4: Simplify the expression

First, calculate the squares: \( (-2)^2 = 4 \) and \( (-2)^2 = 4 \). Then, add them: \( 4 + 4 = 8 \). So, \( d = \sqrt{8} \).

Step5: Approximate the square root

\( \sqrt{8} \approx 2.828 \), and to the nearest tenth, it is \( 2.8 \).

Answer:

The distance between the two points is approximately \( 2.8 \).