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Rectangle ABCD contains a point X such that AX = 1, BX = 7, CX = \(7\).  Find DX.

 Feb 8, 2022
 #1
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DX = AX = 1 laugh

 Feb 8, 2022
edited by Guest  Feb 8, 2022
 #2
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To give a more detailed explanation, since point X is an interior point in rectangle ABCD, and since BX = CX, then triangle BCX is an isosceles triangle. Since ABCD is a rectangle, point X must lie on the line of symmetry of the perpendicular bisector of BC. Thus, ADX is also an isosceles triangle where AX = DX. Because AX = 1, then DX must also be equal to 1.

 

Therefore, DX = 1. smiley

 Feb 8, 2022

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