MATH SOLVE

2 months ago

Q:
# Point C(3.6, -0.4) divides AB in the ratio 3:2. If the coordinates of A are (-6, 5), the coordinates of point B are ___. If point D divides CB in the ratio 4 : 5, the coordinates of point D are ___.

Accepted Solution

A:

when a point divides a line segment into ratios of k1:k2, the formula to find the coordiates of the point is:

x=(k2*x1+k1*x2)/(k1+k2), y=(k2*y1+k1*y2)/(k1+k2),Β

(x1,y1) being the coordinates of the starting point, and (x2,y2) coordinates of the end point.Β

in this case, 3.6=[2*(-6)+3x2]/5

-12+3x2=18

3x2=30

x2=10

use the same method to find y2: -0.4=(2*5+3y2)/5

3y2=-12

y2=-4

so the the coordinates of B is (10,-4)

use the same method to find the coordinates of D.

the answer I've got for D is (58/9, -2) please double check my calculation.

x=(k2*x1+k1*x2)/(k1+k2), y=(k2*y1+k1*y2)/(k1+k2),Β

(x1,y1) being the coordinates of the starting point, and (x2,y2) coordinates of the end point.Β

in this case, 3.6=[2*(-6)+3x2]/5

-12+3x2=18

3x2=30

x2=10

use the same method to find y2: -0.4=(2*5+3y2)/5

3y2=-12

y2=-4

so the the coordinates of B is (10,-4)

use the same method to find the coordinates of D.

the answer I've got for D is (58/9, -2) please double check my calculation.