Question

15 points! please help! Use numerals instead of words. If necessary, use / for the fraction bar(s).

In the given diagram, ∆ABC is a right triangle with . Segment AB is divided into four equal parts.

Answer 1

I got F = (15/4 , -5/2) and G = (-3/4 , -3)

Hope this helps ;)

Explanation:

Answer 2

Point F = (15/4 , -5/2)

Point G = (-3/4 , -3)

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)