Line segment AB¯¯¯¯ has endpoints A(−2,6) and B(4,−6). What are the coordinates of the point that partitions BA¯¯¯¯¯¯¯¯ according to the part-to-part ratio 2:4?

Question

Can someone help me please.

Answer 1

Attach the following to the Desmos URL to get to the graph used in the video answer.

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Answer 2

the distance is sqrt ( (-6)^2 + (-12)^2) = sqrt( 36 + 144) = sqrt( 180) = sqrt(36*5) = 6 * sqrt(5)

2/(2+4) = 2/6 = 1/3

-2 + (1/3)*6*sqrt(5) = -2 + 2* sqrt(5)

6 + (1/3)*6*sqrt(5) = 6 + 2* sqrt(5)