Question

Points P, Q, R and S divide a line segment joining A (2, 6) and B (7, -4) in five equal parts. Find the coordinates of P and R. ​

Answer 1

$\bf{\underline{\underline{Given}}}$

P, Q, R and S divides AB in five equal parts

$\mathsf{Coordinates \: of \: A \: \rightarrow \: (2,6)}$

$\mathsf{Coordinates \: of \: B \: \rightarrow \: (7,-4)}$

$\bf{\underline{\underline{To\:find}}}$

$\mathsf{Coordinates \: of \: P \: and \: R}$

$\bf{\underline{\underline{Solution}}}$

• Case 1 (finding P coordinates)

$\small{\mathsf{P \:divides\: AB\: in\: the\: ratio\:\: 1 : 4}}$

$\mathsf{P(x, y) = \frac{m_{1}x_{2} + m_{2}x_{1}}{m_{1} + m_{2}} , \frac{m_{1}y_{2} + m_{2}y_{1}}{m_{1} + m_{2}}}$

$\mathsf{\implies\: P(x, y) = \frac{1(7) + 4(2)}{1 + 4} , \frac{1(-4) + 4(6)}{1 + 4}}$

$\mathsf{\implies\: P(x, y) = \frac{15}{5} , \frac{20}{5}}$

$\mathsf{\implies\: \green{ P(x, y) = (3, 4)}}$

• Case 2 (finding R coordinates)

$\small{\mathsf{R \:divides \:AB \:in\: the\: ratio\: \:3 : 2}}$

$\mathsf{R(x, y) = \frac{m_{1}x_{2} + m_{2}x_{1}}{m_{1} + m_{2}} , \frac{m_{1}y_{2} + m_{2}y_{1}}{m_{1} + m_{2}}}$

$\mathsf{\implies\: R(x, y) = \frac{3(7) + 2(2)}{3 + 2} , \frac{3(-4) + 2(6)}{3 + 2}}$

$\mathsf{\implies\: R(x, y) = \frac{25}{5} , \frac{0}{5}}$

$\mathsf{\implies\: \green{R(x, y) = (5, 0)}}$

Coordinates of P ➺ (3, 4)

Coordinates of R ➺ (5, 0)

____________________________

Formula Used :

$\fbox{\small{\mathsf{\red{(x, y) = \frac{m_{1}x_{2} + m_{2}x_{1}}{m_{1} + m_{2}} , \frac{m_{1}y_{2} + m_{2}y_{1}}{m_{1} + m_{2}}}}}}$

Answer 2

Answer:

Coordinates:

P = (3,4)

R = (5,0)

Step-by-step explanation:

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