A right triangle is graphed on a coordinate plane. Find the length of the hypotenuse. Round your answer to the nearest tenth.
On coordinate plane, points (2, 4), (2, -3) and (-1, -3) are connected.
To find the length of the hypotenuse, we first need to find the length of the two legs of the triangle.
Using the distance formula:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Leg 1: (2, 4) to (2, -3)
√[(2 - 2)² + (-3 - 4)²]
√[0 + 49]
√49
= 7
Leg 2: (2, -3) to (-1, -3)
√[(2 + 1)² + (-3 - (-3))²]
√[3² + 0]
√9
= 3
Now, we can find the length of the hypotenuse using the Pythagorean theorem:
Hypotenuse² = Leg1² + Leg2²
Hypotenuse² = 7² + 3²
Hypotenuse² = 49 + 9
Hypotenuse² = 58
Hypotenuse = √58
Hypotenuse ≈ 7.6
Therefore, the length of the hypotenuse of the right triangle is approximately 7.6 units.