Question

find the co-ordinates of the point which divides the join of (-1,6)and(4,3) in the ratio 2:3​

Answer 1

Answer:

$(1, {24 \over 5})$

Step-by-step explanation:

Point 1 = (-1, 6)

Point 2 = (4, 3)

Thus,

x1 = -1  &  x2 = 4

y2 = 6  & y2 = 3

Also, ratio = 2:3

Thus,

m1 = 2  &  m2 = 3

By section formula, the coordinates of the point of intersection is:-

$x = {{(m1 \times x2) + (m2 \times x1)}\over{m1 + m2}}\\\\y = {{(m1 \times y2) + (m2 \times y1)}\over{m1 + m2}}$

Thus,

$x = { { 2(4) + 3(-1) } \over {2 + 3} }\\\\y = { { 2(3) + 3(6) } \over {2 + 3} }\\\\\\x = { {8 - 3} \over {5} }\\\\y = { {6 + 18 \over {5} }$

$x = 1\\\\y = {24 \over 5}$

Thus point of intersection = $(1, {24 \over 5})$