Answer:
Explanation:
To find the point that is two-thirds of the way from (-2, -6) to (0, -5), we can use the midpoint formula.
First, let's find the coordinates of the midpoint between (-2, -6) and (0, -5).
To find the x-coordinate of the midpoint, we add the x-coordinates of the endpoints and divide by 2:
((-2) + 0) / 2 = -1
So, the x-coordinate of the midpoint is -1.
To find the y-coordinate of the midpoint, we add the y-coordinates of the endpoints and divide by 2:
((-6) + (-5)) / 2 = -11 / 2 = -5.5
So, the y-coordinate of the midpoint is -5.5.
Now that we have the coordinates of the midpoint, we can find the point that is two-thirds of the way from (-2, -6) to (0, -5).
To find the x-coordinate, we start with the x-coordinate of the midpoint and add two-thirds of the difference between the x-coordinates of the endpoints:
-1 + (2/3)(0 - (-2)) = -1 + (2/3)(2) = -1 + (4/3) = -1 + 1.333 = 0.333
So, the x-coordinate of the point that is two-thirds of the way is approximately 0.333.
To find the y-coordinate, we start with the y-coordinate of the midpoint and add two-thirds of the difference between the y-coordinates of the endpoints:
-5.5 + (2/3)(-5 - (-6)) = -5.5 + (2/3)(1) = -5.5 + (2/3) = -5.5 + 0.667 = -4.833
So, the y-coordinate of the point that is two-thirds of the way is approximately -4.833.
Therefore, the point that is two-thirds of the way from (-2, -6) to (0, -5) is approximately (0.333, -4.833).