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Points P, Q, R and S divide the line segment joining the point

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

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Points P, Q, R and S divide the line segment joining the points

A (1, 2)

and

B (6, 7)

in five equal parts. Find the coordinates of the points P, Q and R.

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Text solutionVerified

Given: Points P, Q, R and S divides a line segment joining the points

A (1, 2)

and

B (6, 7)

5

equal parts. We know that:

x = \frac{m _{1} x _{2} + m _{2} x _{1}}{m _{1} + m _{2}}

y = \frac{m _{1} y _{2} + m _{2} y _{1}}{m _{1} + m _{2}}

Now,

Step

1

: Find coordinates of P.

P (x, y)

divides AB in the ratio

1 : 4

x = (1 \times 6 + 4 \times 1) /1 + 4

= (6 + 4) /5

= 10/5

= 2

y (1 \times 7 + 4 \times 2) /5

= (7 + 8) /5

= 15/5

= 3

So,

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

Step

2

: Find coordinates of Q.

Q divides the segment AB in ratio

2 : 3

x = (2 \times 6 + 3 \times 1) /5

= (12 + 3) /5

= 15/5 = 3

y = (2 \times 7 + 3 \times 2) /5

= (14 + 6) /5

= 20/5 = 4

So,

Q (x, y) = Q (3, 4)

Step

3

: Find coordinates of R.

R divides the segment AB in ratio

3 : 2

x = (3 \times 6 + 2 \times 1) /5

= (18 + 2) /5

= 20/5

= 4

y = (3 \times 7 + 2 \times 2) /5

= (21 + 4) /5

= 25/5

= 5

So,

R (x, y) = R (4, 5)

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Question Text	Points P, Q, R and S divide the line segment joining the points $A (1, 2)$ and $B (6, 7)$ in five equal parts. Find the coordinates of the points P, Q and R.
Answer Type	Text solution:1
Upvotes	150

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

Text solutionVerified

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