Answer:
The coordinates of point A are (-11 , 2)
Step-by-step explanation:
- The coordinates of point P are (-31 , 8)
- The coordinates of point H are (29 , -10)
- Point E is the mid-point of segment PH
- The coordinates of the the mid-point are:
→
and ![y=\frac{y_{1}+y_{2}}{2}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7By_%7B1%7D%2By_%7B2%7D%7D%7B2%7D)
∵ E is the mid-point of segment PH
∴ The x-coordinate of point E is ![x=\frac{-31+29}{2}=-1](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-31%2B29%7D%7B2%7D%3D-1)
∴ The x-coordinate of point E is -1
∴ The y-coordinate of point E is ![y=\frac{8+-10}{2}=-1](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B8%2B-10%7D%7B2%7D%3D-1)
∴ The y-coordinate of point E is -1
∴ The coordinates of point E are (-1 , -1)
- Point A is graphed
of the way along the segment from P to E
- That mean the distances from points P to A is 2 parts and from P to E
is 3 parts, then the distance from A to E is "3 - 2" = 1 part
- So point A divides the line segment PE at ratio 2 : 1 from P
- The coordinates of the division point are:
→
and ![y=\frac{y_{1}m_{2}+y_{2}m_{1}}{m_{1}+m_{2}}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7By_%7B1%7Dm_%7B2%7D%2By_%7B2%7Dm_%7B1%7D%7D%7Bm_%7B1%7D%2Bm_%7B2%7D%7D)
∵ Point A divides PE at ratio 2 : 1
∵ The coordinates of point P are (-31 , 8)
∵ The coordinates of point E are (-1 , -1)
∴ The x-coordinate of point A is ![x=\frac{(-31)(1)+(-1)(2)}{2+1}= -11](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B%28-31%29%281%29%2B%28-1%29%282%29%7D%7B2%2B1%7D%3D%20-11)
∴ The x-coordinate of point A is -11
∴ The y-coordinate of point A is ![x=\frac{(8)(1)+(-1)(2)}{2+1}=2](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B%288%29%281%29%2B%28-1%29%282%29%7D%7B2%2B1%7D%3D2)
∴ The y-coordinate of point A is 2
∴ The coordinates of point A are (-11 , 2)
* The coordinates of point A are (-11 , 2)