Answer:
Point F = (15/4 , -5/2)
Point G = (-3/4 , -3)
Step-by-step explanation:
* From the figure
- AB divided into 4 equal parts, so that:
# E is the mid-point of AB
# D is the mid-point of AE
# F is the mid-point of EB
* Lets revise the rule of the mid-point
- If M (x , y) is the mid-point of the segment AB, where A (x1 , y1)
and B (x2 , y2)
∴ x = (x1 + x2)/2 and y = (y1 + y2)/2
* Now we can find points E , F , D
∵ A (-3 , -1) and B (6 , -3), E is the mid-point of AB
∴ E =[(-3 + 6)/2 , (-1 + -3)/2] = (3/2 , -2)
∵ F is the mid-point of EB , E (3/2 , -2) , B (6 , -3)
∴ F = [(3/2 + 6)/2 , (-2 + -3)/2] = (15/4 , -5/2)
∵ D is the mid-point of AE , A (-3 , -1) , E (3/2 , -2)
∴ D = [(-3 + 3/2)/2 , (-1 + -2)/2] = (-3/4 , -3/2)
* From the graph DG ⊥ BC
∵ BC is a horizontal segment because B and C have same y coordinate
∵ G lies on BC
∴ The y-coordinate of G is the same of y-coordinate of B and C
∴ The y-coordinate of G is -3
∵ DG ⊥ BC
∴ DG is a vertical segment
∴ G has the same x-coordinate of D
∴ The x-coordinate of G is -3/4
∴ G = (-3/4 , -3)
