Description
WZ has end points w(-3,-8) and z(5,12). point x lies between w and z such that wx+1/4 find the coordinates of x.
the answer is x+(3/4)w+(1/4)z but i don't know how the answer was found
Explanation & Answer
Thank you for the opportunity to help you with your question!
By Using the midpoint formula, we can find the midpoint of WZ. If we call that midpoint P, finding the midpoint of WP will give us the required point X such that WX = (1/4)WZ.
With using midpoint formula, the midpoint of WZ is:
P = ((-3 + 5)/2, (-8 + 12)/2) = (1, 2).
Now, the midpoint of WP is:
X = ((-3 + 1)/2, (-8 + 2)/2) = (-1, -3).
As a check:
WZ = √[(-3 - 5)^2 + (-8 - 12)^2] = √(64 + 400) = 4√29
WX = √[(-3 + 1)^2 + (-8 + 3)^2] = √(4 + 25) = √29 = (1/4)WZ.