Final answer:
The lengths between points on a coordinate plane can be calculated using the distance formula, which is based on the Pythagorean theorem. You find the square root of the sum of the squares of the differences in x and y coordinates to determine the distance between each pair of points.
Step-by-step explanation:
The question involves calculating the lengths of sides between four given points using the distance formula. The distance formula is derived from the Pythagorean theorem and can be stated as the square root of the sum of the squares of the differences in the x-coordinates and y-coordinates of two points. Specifically, for two points (x1, y1) and (x2, y2), the distance is given by √((x2 - x1)2 + (y2 - y1)2).
To find the length of the side between point (-1,2) and (4,4), we calculate the following:
- √((4 - (-1))2 + (4 - 2)2)
- = √((5)2 + (2)2)
- = √(25 + 4)
- = √29
- ≅ 5.39 units
This process is repeated for the other pairs of points to determine the lengths of the remaining sides. This is a common task in geometry that often requires the Pythagorean theorem for right triangles.