Points P, Q, R and S divide the line segment joining the points A (1, 2) and B(6, 7) into five equal parts. Find the coordinates of the points P, Q and R.

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Solution

P divides AB in the ratio is 1:4

Coordinates of P using section formula,

using Section Formula given by.
$open parentheses fraction numerator x subscript 1 n plus x subscript 2 m over denominator m plus n end fraction comma fraction numerator y subscript 1 n plus y subscript 2 m over denominator m plus n end fraction close parentheses$
Here m = 1 and n = 4, = 6, = 1, = 7, = 2

$x equals fraction numerator 1 cross times 6 plus 4 cross times 1 over denominator 1 plus 4 end fraction equals 2 space comma y equals fraction numerator 1 cross times 7 plus 4 cross times 2 over denominator 1 plus 4 end fraction equals 3$

Coordinates of P (2,3).

Q divides AB in the ratio is 2:3

Coordinates of Q

$x equals fraction numerator 2 cross times 6 plus 3 cross times 1 over denominator 2 plus 3 end fraction equals 3 comma y equals fraction numerator 2 cross times 7 plus 3 cross times 2 over denominator 2 plus 3 end fraction equals 4$

Coordinates of Q are (3,4)

R divides AB in the ratio is 3:2

Coordinates of R are

$x equals fraction numerator 3 cross times 6 plus 2 cross times 1 over denominator 3 plus 2 end fraction equals 4 comma y equals fraction numerator 3 cross times 7 plus 2 cross times 2 over denominator 3 plus 2 end fraction equals 5$
Coordinates of R are (4,5)

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