Question

Point D is the midpoint of IK. ID = 17x – 4 and DK = 8x + 23. Determine the length of IK.

A) 10x - 19
B) 12x + 19
C) 25x - 27
D) 25x - 46

Answer 1

The length of IK is 47 units.

Step-by-step explanation:

Given that point D is the midpoint of IK, we know that the distance from I to D is equal to the distance from D to K. Let's set up an equation to solve for x.

ID = DK

17x - 4 = 8x + 23

Now, we can solve for x. Subtracting 8x from both sides and adding 4 to both sides, we get:

9x = 27

x = 3

Now, we substitute the value of x back into the expressions for ID and DK to find the length of IK:

ID = 17x - 4 = 17(3) - 4 = 47

DK = 8x + 23 = 8(3) + 23 = 47

Therefore, the length of IK is 47 units.