Graphing a Right Triangle and Calculating Distance
The provided image shows a coordinate grid with the task to graph a right triangle with two points given: (5,2) and (2,-2), with these points forming the hypotenuse. To graph the right triangle, the third point should form a right angle with the given points.
To find the third point, you can keep either the x-coordinate (5) the same and change the y-coordinate to -2, or keep the y-coordinate (2) the same and change the x-coordinate to 2. This will create a right angle at the third point. Let's use the first option and have the third point be (5, -2).
Now to find the distance between the two points (5,2) and (2,-2) using the Pythagorean theorem, you calculate the lengths of the other two sides of the triangle and then apply the theorem a^2 + b^2 = c^2.
The length of the triangle's side that lies along the x-axis (horizontal side) is the difference between the x-coordinates of the two points: |5 - 2| = 3.
The length of the side that lies along the y-axis (vertical side) is the difference between the y-coordinates of the two points: |2 - (-2)| = |2 + 2| = 4.
Now plug these values into the Pythagorean theorem to find the hypotenuse:
a^2 + b^2 = c^2
3^2 + 4^2 = c^2
9 + 16 = c^2
25 = c^2
c = √25
c = 5
Therefore, the distance between the two points (5,2) and (2,-2) is 5 units.
