Segment ph is graphed on the coordinate grid where p is (-31,8) and h is (29,-10). point e is the midpoint of segment ph. if point a is graphed 2/3 of the way along the segment from p to e, then what are the coordinates of point a?

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)

"if it is my birthday, then it is snowing"