Find the coordinates of point E if C is the midpoint of AE.

- A has the coordinates of (-3, 1)
- C has the coordinates of (-2, -1)

coor d ina t es o f E ( x , y ) mi d p o in t : C ( − 2 , − 1 ) e n d p o in t : A ( − 3 , 1 ) B ( − 2 , − 1 ) = ( 2 − 3 + x ​ ; 2 1 + y ​ ) − 2 = 2 − 3 + x ​ ∣ m u lt i pl y b y 2 − 4 = − 3 + x ∣ a dd 3 − 1 = x − 1 = 2 1 + y ​ ∣ m u lt i pl y b y 2 − 2 = 1 + y ∣ s u b t r a c t 1 − 3 = y C oor d ina t e o f C = ( − 1 , − 3 )

Answered by luana | 2024-06-10

The coordinates of point E are (-1, -3).
The question asks us to find the coordinates of point E given that A has the coordinates of (-3,1), C is the midpoint of AE with coordinates (-2,-1), and to find the coordinates of E when C is the midpoint. We can solve this by using the midpoint formula which states that the midpoint C's coordinates are the averages of the coordinates of A and E. Thus, the x-coordinate of point E can be found by multiplying the x-coordinate of C by 2 and then subtracting the x-coordinate of A, and similarly for the y-coordinate. We find E's coordinates by the steps below:
Calculate the x-coordinate: (2 \times -2) - (-3) = -4 + 3 = -1.
Calculate the y-coordinate: (2 \times -1) - 1 = -2 - 1 = -3.
Therefore, the coordinates of point E are (-1, -3).

Answered by YashBhattar | 2024-06-24

To find the coordinates of point E when C is the midpoint of AE, we can use the midpoint formula. By solving the equations derived from the known coordinates of A and C, we find that E has coordinates (-1, -3).
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Answered by luana | 2024-09-27