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:
→ [tex]x=\frac{x_{1}+x_{2}}{2}[/tex] and [tex]y=\frac{y_{1}+y_{2}}{2}[/tex]
∵ E is the mid-point of segment PH
∴ The x-coordinate of point E is [tex]x=\frac{-31+29}{2}=-1[/tex]
∴ The x-coordinate of point E is -1
∴ The y-coordinate of point E is [tex]y=\frac{8+-10}{2}=-1[/tex]
∴ The y-coordinate of point E is -1
∴ The coordinates of point E are (-1 , -1)
- Point A is graphed [tex]\frac{2}{3}[/tex] 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:
→ [tex]x=\frac{x_{1}m_{2}+x_{2}m_{1}}{m_{1}+m_{2}}[/tex] and [tex]y=\frac{y_{1}m_{2}+y_{2}m_{1}}{m_{1}+m_{2}}[/tex]
∵ 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 [tex]x=\frac{(-31)(1)+(-1)(2)}{2+1}= -11[/tex]
∴ The x-coordinate of point A is -11
∴ The y-coordinate of point A is [tex]x=\frac{(8)(1)+(-1)(2)}{2+1}=2[/tex]
∴ The y-coordinate of point A is 2
∴ The coordinates of point A are (-11 , 2)
* The coordinates of point A are (-11 , 2)
