Find the point that is one-fourth of the way from P=(2,-5,3) to Q=(1,-2,5). Please show step-by-step, this way I can learn it. Thank you.
for each coordinate, add 1/4 of the difference between P and Q. For example, using the x coordinate, Q-P = 1-2 = -1
So, add -1/4 to P, and the new x-coordinate is 1.75
similarly for y and z.
To find the point that is one-fourth of the way from P=(2,-5,3) to Q=(1,-2,5), we can use the formula for finding a point on a line segment between two given points.
Let's call the point we're looking for R. The coordinates of R will be (x, y, z).
Step 1: Calculate the differences between the coordinates of P and Q.
Δx = xQ - xP = 1 - 2 = -1
Δy = yQ - yP = -2 - (-5) = 3
Δz = zQ - zP = 5 - 3 = 2
Step 2: Multiply each difference by 1/4 to find the one-fourth distance.
Δx/4 = -1/4
Δy/4 = 3/4
Δz/4 = 2/4 = 1/2
Step 3: Add the one-fourth distances to the coordinates of P.
xR = xP + Δx/4 = 2 + (-1/4) = 7/4
yR = yP + Δy/4 = -5 + (3/4) = -17/4
zR = zP + Δz/4 = 3 + (1/2) = 7/2
So, the point R that is one-fourth of the way from P to Q is (7/4, -17/4, 7/2).