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

Answer:

B = (10, -4),  D = (58/9, -2)

Step-by-step 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:

$x=\frac{n}{n+m}(x_2-x_1)+x_1 ;\ y=\frac{n}{n+m}(y_2-y_1)+y_1$

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

$3.6=\frac{3}{3+2}(x_2-(-6))-6\\\\9.6=\frac{3}{5}(x_2+6) \\\\x_2+6=16\\\\x_2=10\\\\\\-0.4=\frac{3}{3+2}(y_2-5)+5\\\\-5.4=\frac{3}{5}(y_2-5) \\\\y_2-5=-9\\\\y_2=-4$

B = (10, -4)

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

$x=\frac{4}{4+5}(10-3.6)+3.6 \\\\x=\frac{58}{9} \\\\\\y=\frac{4}{4+5}(-4-(-0.4))+(-0.4)\\\\y=-2$

Hence D = (58/9, -2)