Question

What is the x-coordinate of the point that divides the directed line segment from J to K into a ratio of 2:5?

a) 2
b) -4
c) -2
d) 4

Answer 1

To find the x-coordinate of the point that divides the directed line segment from J to K into a ratio of 2:5, we can use the concept of ratio and proportion. The x-coordinate is given by (5xJ + 2xK)/7.

Step-by-step explanation:

To find the x-coordinate of the point that divides the directed line segment from J to K into a ratio of 2:5, we can use the concept of ratio and proportion. Let's assume the x-coordinate of point J is xJ and the x-coordinate of point K is xK. According to the given ratio, we can set up the following proportion: 2/5 = (x - xJ)/(xK - x). Cross multiplying, we get 5(x - xJ) = 2(xK - x). Simplifying, we have 5x - 5xJ = 2xK - 2x. Rearranging the equation, we get 5x + 2x = 5xJ + 2xK. Combining like terms, we have 7x = 5xJ + 2xK. Dividing both sides by 7, we get x = (5xJ + 2xK)/7. Therefore, the x-coordinate of the point that divides the segment into a ratio of 2:5 is (5xJ + 2xK)/7.