Can you and need the work to show how you go it.

Point Q is (3 , 4)

Step-by-step explanation:

* Lets revise the rule of the point which divides of a line segment in

 a ratio

- If point (x , y) divides the line segment AB, where A is (x1 , y1) and

 B is (x2 , y2) in the ratio m1 : m2

∴ x = [m2(x1) + m1(x2)]/(m1 + m2)

∴ y = [m2(y1) + m1(y2)]/(m1 + m2)

* Now lets solve the problem

- Point Q divides ST in the ratio 5 : 2 where S (-2 , -6) and T (5 , 8)

- To find the coordinates of point Q use the same rule above

# Q is (x , y)

# S is (x1 , y1) and T is (x2 , y2)

# m1 : m2 is 5 : 2

∵ x1 = -2 and y1 = -6

∵ x2 = 5 and y2 = 8

∵ m1 = 5 and m2 = 2

- Substitute these values in the rule

∵ x = [m2(x1) + m1(x2)]/(m1 + m2)

∴ x = [2(-2) + 5(5)]/(5 + 2) ⇒ multiply the numbers

∴ x = [-4 + 25]/7 ⇒ add

∴ x = [21]/7 ⇒ Divide

∴ x = 3

* The x-coordinate of Q is 3

∵ y = [m2(y1) + m1(y2)]/(m1 + m2)

∴ y = [2(-6) + 5(8)]/(5 + 2) ⇒ multiply the numbers

∴ y = [-12 + 40]/7 ⇒ add

∴ y = [28]/7 ⇒ Divide

∴ y = 4

* The y-coordinate of point Q is 4

∴ Point Q is (3 , 4)

the answer is (-4,-4)

hope this ! : d