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PIT_PIT [208]
3 years ago
6

Find the coordinates of point B along a directed line segment from A(3,4) and

Mathematics
1 answer:
andreev551 [17]3 years ago
8 0

We have been given two points. A(3,4) and C(3,9). We are asked to find the point B such that it divides line segment AC so that the ratio of AB to BC is 4:1.

We will use segment formula to solve our given problem.

When a point P divides segment any segment internally in the ratio m:n, then coordinates of point P are:

[\right x=\frac{mx_2+nx_1}{m+n},y=\frac{my_2+ny_1}{m+n}\left]

(x_1,y_1)=(3,4) and (x_2,y_2)=(3,9).

m=4,n=1

Upon substituting our given information in above formula, we will get:

[\right x=\frac{4(3)+1(3)}{4+1},y=\frac{4(9)+1(4)}{4+1}\left]

[\right x=\frac{12+3}{5},y=\frac{36+4}{5}\left]

[\right x=\frac{15}{5},y=\frac{40}{5}\left]

[\right x=3,y=8\left]

Therefore, the coordinates of point B would be (3,8).

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