Question

Point C (3,6, -0,4) divides AB in the ratio 3:2. If the coordinates of point B are. If point D divides CB in the ratio 4:5, the coordinates of point D are

Answer 1

B = (10, -4), D = (58/9, -2)

Explanation:

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

Solution:

If point O(x, y) divides line segment AB with endpoints at A(x₁, y₁) and B(x₂, y₂) in the ratio n:m, then:

`x=(n)/(n+m)(x_2-x_1)+x_1 ;\ y=(n)/(n+m)(y_2-y_1)+y_1`

Since point C divides AB in the ratio 3:2. Let the coordinates of B be (x₂, y₂). Hence:

`3.6=(3)/(3+2)(x_2-(-6))-6\\\\9.6=(3)/(5)(x_2+6) \\\\x_2+6=16\\\\x_2=10\\\\\\-0.4=(3)/(3+2)(y_2-5)+5\\\\-5.4=(3)/(5)(y_2-5) \\\\y_2-5=-9\\\\y_2=-4`

B = (10, -4)

D divides CB in the ratio 4:5. Let D = (x, y). Hence:

`x=(4)/(4+5)(10-3.6)+3.6 \\\\x=(58)/(9) \\\\\\y=(4)/(4+5)(-4-(-0.4))+(-0.4)\\\\y=-2`

Hence D = (58/9, -2)