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 
∵ E is the mid-point of segment PH
∴ The x-coordinate of point E is 
∴ The x-coordinate of point E is -1
∴ The y-coordinate of point E is 
∴ 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 
∵ 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 
∴ The x-coordinate of point A is -11
∴ The y-coordinate of point A is 
∴ The y-coordinate of point A is 2
∴ The coordinates of point A are (-11 , 2)
* The coordinates of point A are (-11 , 2)
