Question

In triangle ABC, given that point A is located at coordinates (4, 5), point B at coordinates (3, 3), and point C at coordinates (5, 2), what is the length of side AB of the triangle?

a. 56
b. 3
c. 118
d. 6

Answer 1

To find the length of side AB of the triangle, we use the distance formula, which results in a calculation of √5 or ≃5, which is none of the given options.

Step-by-step explanation:

The student is asking how to find the length of side AB in triangle ABC given the coordinates of points A and B. To calculate the distance between two points (x1, y1) and (x2, y2) in a coordinate plane, we can use the distance formula which is derived from the Pythagorean theorem: √((x2 - x1)² + (y2 - y1)²). Applying this formula to points A(4, 5) and B(3, 3), we get the length of side AB as √((3 - 4)² + (3 - 5)²), which simplifies to √((-1)² + (-2)²) = √(1 + 4) = √5 = ≃5. Since none of the answer choices match this result, the student may have made a typo or there could be an error in the given options.