15 points! ! 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.

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)

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is

answer:

c) the x-coordinate of the center of the circle increases by 3