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tinalmath
22.06.2019 •
Mathematics
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?
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Ответ:
The x-coordinate of Q is 5
Step-by-step 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:
#![x=\frac{m_{2}x_{1}+m_{1}x_{2}}{m_{1}+m_{2}}](/tpl/images/0003/2286/6e2fe.png)
#![y=\frac{m_{2}y_{1}+m_{1}y_{2}}{m_{1}+m_{2}}](/tpl/images/0003/2286/6a8df.png)
* 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=\frac{(3)(-3)+(1)(x_{2})}{1+3}=\frac{-9+x_{2}}{4}](/tpl/images/0003/2286/9a092.png)
- By cross multiplication
∴ (-1) (4) = -9 + x2
∴ -4 = -9 + x2 ⇒ add 9 to both sides
∴ 5 = x2
* The x-coordinate of Q is 5
Ответ:
It's a parabola opening up from the vertex (4,5) and intercepts the y-axis at (0,37)