Question

The three vertices of a triangle are given as (-2, -1), (-2, 3), and (1, 3). Calculate the length of the longest side of the triangle.

Answer 1

The longest side of the triangle formed by the points (-2, -1), (-2, 3), and (1, 3) is the side AC, measuring 5 units. This is determined using the distance formula derived from the Pythagorean theorem.

Step-by-step explanation:

To calculate the length of the longest side of the triangle with vertices (-2, -1), (-2, 3), and (1, 3), we can use the distance formula between two points in a coordinate plane, which is based on the Pythagorean theorem: d = √((x2 - x1)² + (y2 - y1)²).

Let’s label our points A(-2, -1), B(-2, 3), and C(1, 3). We will calculate the length of the sides of the triangle, AB, BC, and AC.

1. AB: Since both points A and B have the same x-coordinate, (-2), we can find the distance between them by simply subtracting the y-coordinates. AB = |3 - (-1)| = 4 units.
2. BC: Similarly, points B and C have the same y-coordinate, (3), so the distance between them is the difference in x-coordinates. BC = |1 - (-2)| = 3 units.
3. AC: To find the distance between points A and C, we use the distance formula since they have different x and y-coordinates. AC = √((1 - (-2))² + (3 - (-1))²) = √((3)² + (4)²) = √(9 + 16) = √25 = 5 units.

The longest side of the triangle is AC, which measures 5 units.