Rectangle ABCDABCDA, B, C, D is graphed in the coordinate plane. The following are the vertices of the rectangle: A(2, 1)A(2,1)A
, left parenthesis, 2, comma, 1, right parenthesis, B(5, 1)B(5,1)B, left parenthesis, 5, comma, 1, right parenthesis, C(5, 6)C(5,6)C, left parenthesis, 5, comma, 6, right parenthesis, and D(2, 6)D(2,6)D, left parenthesis, 2, comma, 6, right parenthesis. Given these coordinates, what is the length of side ABABA, B of this rectangle?
1 answer:
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9514 1404 393
Answer:
x = √(w(w+z))
Step-by-step explanation:
The idea with a right-triangle figure of this sort is that all of the triangles are similar. Here, x is the short side of ∆ABC, and the hypotenuse of ∆BDC. This suggests you want to write a similarity statement involving the short side and hypotenuse.
BC/AC = DC/BC . . . . . short side/hypotenuse
BC² = AC·DC . . . . . . cross multiply
x² = (w+z)w . . . . . . substitute letter values
Taking the square root and rearranging to the form of the applicable answer choice, this is ...