Question

(5,-6)(4,5)3:4 find the point that partitions the segment with the two given endpoints with the given ratio

Answer 1

The points given are (5, -6) and (4, 5).

Let the points be A and B.

The line segment is partitioned in the ratio 3 : 4, therefore we can call the point of the partition L.

`\begin{gathered} (x_1,y_1)=(5,-6) \\ (x_2,y_2)=(4,5) \\ a\colon b=3\colon4 \\ (b(x_1)+a(x_2))/(a+b),(b(y_1)+a(y_2))/(a+b) \\ \text{Substitute for the values and you now have;} \\ L=(4(5)+3(4))/(3+4),(4(-6)+3(5))/(3+4) \\ L=(20+12)/(7),(-24+15)/(7) \\ L=(32)/(7),(-9)/(7) \end{gathered}`

The coordinates (points) that partitions the given endpoints in the ratio 3:4 are

(32/7, -9/7)