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).
left bracket, minus, 1, comma, 2, right bracket, and , left bracket, 2, comma, 5, right bracket
(−1,2) and (2,5)
Leg 1: 3, Leg 2: 3, Distance: ?
To graph the right triangle, plot the points (-1,2) and (2,5) on a coordinate plane.
Plot the point (-1,2) as (-1,2) on the coordinate plane. Then, plot the point (2,5) as (2,5) on the coordinate plane.
Next, draw a line connecting the two points to form the hypotenuse of the right triangle.
Now, calculate the lengths of the two legs.
Leg 1: The change in the x-coordinate is 2 - (-1) = 3, and the change in the y-coordinate is 5 - 2 = 3. Therefore, the length of Leg 1 is √(3^2 + 3^2) = √18 ≈ 4.2.
Leg 2: The change in the x-coordinate is 2 - (-1) = 3, and the change in the y-coordinate is 5 - 2 = 3. Therefore, the length of Leg 2 is √(3^2 + 3^2) = √18 ≈ 4.2.
Finally, calculate the distance between the two points, which is the length of the hypotenuse of the right triangle. The length of the hypotenuse is also √(3^2 + 3^2) = √18 ≈ 4.2.