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Question

In the figure shown, a perpendicular segment is drawn from B in rectangle ABCD to meet diagonal AC at point X. Side AB is 6 cm and diagonal AC is 10 cm. How many centimeters away is point X from the midpoint M of the diagonal AC? Express your answer as a decimal to the nearest tenth.

Accepted Answer

We see that ABX ACB since BXA = ABC and A is shared by both triangles. From this similarity, we have the equation ABAC=AXAB. Plugging in the known values of the sides and solving for AX, we have 610=AX6 AX=3.6. Since AM=10/2=5, XM=5-3.6=1.4 centimeters.