AP ICET 2019 Shift 1 Paper

Question : 139 of 200

Marks: +1, -0

If A(3, 10), B (-3,4) and C (5,8) are the vertices of a ΔABC and AD and CF are its medians, then the ratio of the length of AD to the length of CF is

Solution:

In ΔABC, AD is median on BC
⇒ D is the midpoint of BC.∴D = (1, 6)
Similarly F = (0, 7).

A D=√{(3-1)^{2}+(10-6)^{2}}=√{20}

CF=√{(5-0)^{2}+(8-7)^{2}}=√{26}

A D: C F=√{20}: √{26}=√{10}: √{13}

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