Final answer:
To determine the length of a side of the rhombus ABCD, we can use the distance formula based on the Pythagorean theorem to calculate the distance between two adjacent vertices such as A and B, which results in the length √17 units.
Step-by-step explanation:
To find the length of a side of the rhombus ABCD with vertices A(-2,3), B(-1,7), C(3,8), and D(2,4) using the algebraic method, we can calculate the distance between two adjacent vertices, such as A and B. We will use the distance formula which is derived from the Pythagorean theorem:
Distance between two points (x1, y1) and (x2, y2) is given by:
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Applying this formula to points A and B:
AB = √[(-1 - (-2))^2 + (7 - 3)^2]
AB = √[(1)^2 + (4)^2]
AB = √[1 + 16]
AB = √[17]
The length of side AB is √17 units.
Since all sides of a rhombus are equal, the length of each side of rhombus ABCD is √17 units.