Answer:
Point Q is (3 , 4)
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)