Answer:
MD = 2 × DN
Step-by-step explanation:
The ratio of interest is MD/DN. It can be found by considering either the x-coordinates or the y-coordinates.
Ratio
The ratio of interest is ...
MD/DN = (D -M)/(N -D)
= ((2, 4/3) -(-6, -4))/((6, 4) -(2, 4/3)) = (2 +6, 4/3 +4)/(6 -2, 4 -4/3)
= (8, 16/3)/(4, 8/3) = (8/4, 16/8) = (2, 2)
The ratio 2 relates MD to DN. That is MD is twice as long as DN.
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Additional comment
The ratio based on x-coordinates is the same as that based on y-coordinates, as it should be. Effectively, this is a check that D lies on MN and that we did the calculation correctly.
