Question

Consider the points A (3,7) and B (11, -5). What are the coordinates of C so that C is on the line segment AB with AC:CB = 7:1? Thanks in advance!!!

Answer 1

`C=(10,-7/2)`

Explanation:

`"given a line with endpoints"`

`A(x_1,y_1)" and "B(x_2,y_2)" being sectioned by a point C"`
`"in the ratio m:n"`

`"then using the "color(blue)"section formula"`

`•color(white)(x)C=[(mx_2+nx_1)/(m+n),(my_2+ny_1)/(m+n)]`

`"here "(x_1,y_1)=(3,7),(x_2,y_2)=(11,-5)`

`"and "m:n=7:1`

`C=[((7xx11)+(1xx3))/(7+1),((7xx-5)+(1xx7))/(7+1)]`

`color(white)(C)=(80/8,-28/8)=(10,-7/2)`