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). (5, 8) and (9, 4) click twice to draw a line. click a segment to erase it.

Explanation:

Step1: Identify the coordinates

Let the two points be \((x_1, y_1) = (5, 8)\) and \((x_2, y_2) = (9, 4)\).

Step2: Calculate the differences in coordinates

The horizontal difference (along x - axis) is \(a=x_2 - x_1=9 - 5 = 4\).
The vertical difference (along y - axis) is \(b=y_1 - y_2=8 - 4 = 4\) (we take absolute value, so order doesn't matter for length).

Step3: Apply the Pythagorean theorem

For a right triangle with legs \(a\) and \(b\) and hypotenuse \(c\) (the distance between the two points), the formula is \(c=\sqrt{a^{2}+b^{2}}\).
Substitute \(a = 4\) and \(b = 4\) into the formula:
\(c=\sqrt{4^{2}+4^{2}}=\sqrt{16 + 16}=\sqrt{32}\)

Step4: Simplify and round

\(\sqrt{32}\approx5.7\) (since \(\sqrt{32}=4\sqrt{2}\approx4\times1.414 = 5.656\approx5.7\) when rounded to the nearest tenth)

Answer:

The distance between the two points \((5,8)\) and \((9,4)\) is approximately \(5.7\).