Question

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar. The endpoints of AB are A(1.4) and B(6,-1). If point C divides AB in the ratio 2:3, the coordinates of point Care If point D divides AC in the ratio 3:2. the coordinates of point D are 6:2 Reset Next ts reserved.

Answer 1

Step-by-step explanation

Mathematically, if a point C(x, y) divides the coordinates A(x₁, y₁) and B(x₂, y₂) internally in the ratio m:n then point C(x, y) is given as

x = [(mx₂ + nx₁)/(m + n)]

y = [(my₂ + ny₁)/(m + n)]

For this question,

(x₁, y₁) and (x₂, y₂) are A (1, 4) and B (6, -1)

Ratio = m : n = 2 : 3

x₂ = 6

x₁ = 1

y₂ = -1

y₁ = 4

m = 2

n = 3

x = [(mx₂ + nx₁)/(m + n)]

x = [(2×6 + 3×1)/(2 + 3)]

x = [(12 + 3)/(5)]

x = (15/5) = 3

y = [(my₂ + ny₁)/(m + n)]

y = [(2×-1 + 3×4)/(2 + 3)]

y = [(-2 + 12)/(5)]

y = (10/5) = 2

So, the coordinates of point , the corrdinatesC which divide A (1, 4) and B (6, -1) into the ratio 2:3 is

C (x, y) = C (3, 2)

Point D divides