Triangle IJK was created by plotting three points and connecting them on a coordinate grid. Which set of coordinates are located on line segment IK? Responses A (7,6)(7,6) B (6,9)(6,9) C (6,4)(6,4) D (5,3)(5,3)
To determine which set of coordinates are located on line segment IK, we need to find the slope of the line passing through points I and K.
The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Let's find the slope of the line passing through points I(7, 6) and K(5, 3):
m = (3 - 6) / (5 - 7)
m = (-3) / (-2)
m = 3/2
Now we need to check which set of coordinates have a slope of 3/2 when connected with point I (7, 6).
Checking each option, we have:
Option A: (7, 6) and (7, 6)
m = (6 - 6) / (7 - 7)
m = 0 / 0
The slope is undefined (division by zero), so option A is NOT on line segment IK.
Option B: (6, 9) and (6, 9)
m = (9 - 6) / (6 - 7)
m = 3 / -1
The slope is not equal to 3/2, so option B is NOT on line segment IK.
Option C: (6, 4) and (6, 4)
m = (4 - 6) / (6 - 7)
m = -2 / -1
The slope is positive 2, so option C is NOT on line segment IK.
Option D: (5, 3) and (5, 3)
m = (3 - 6) / (5 - 7)
m = -3 / -2 = 3/2
The slope is equal to 3/2, so option D IS on line segment IK.
Therefore, the correct answer is option D: (5, 3)(5, 3).