Question

Point R divides PO in the ratio 1:3. If the x-coordinate of R is -1 and the x-coordinate of P is-3, what is the x-coordinate of Q?

Answer 1

The x-coordinate of Q is 5

Explanation:

* Lets revise the division of the line segment

- If point (x , y) divides a line segment internally whose endpoints are

(x1 , y1) and (x2 , y2) at the ratio m1 : m2 from (x1 , y1), then:

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`x=(m_(2)x_(1)+m_(1)x_(2))/(m_(1)+m_(2))`

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`y=(m_(2)y_(1)+m_(1)y_(2))/(m_(1)+m_(2))`

* Lets solve the problem

∵ Point R divides PQ in the ratio 1 : 3

∴ R is (x , y)

∴ P is (x1 , y1) and Q is (x2 , y2)

∴ m1 = 1 and m2 = 3

∵ x-coordinate of R is -1 and the x-coordinate of P is -3

∴ x = -1

∴ x1 = -3

- Use the rule above

∵
`-1=((3)(-3)+(1)(x_(2)))/(1+3)=(-9+x_(2))/(4)`

- By cross multiplication

∴ (-1) (4) = -9 + x2

∴ -4 = -9 + x2 ⇒ add 9 to both sides

∴ 5 = x2

* The x-coordinate of Q is 5