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If rhombus ABCD had vertices A(-2,3),B(-1,7),C(3,8),D(2,4). Using the algebraic method, what is the length of a side of this rhombus?

User Diandra
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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.

User Edward Yang
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