Find the point that is one-fourth of the way from (2,4) to (10,8).
let the point be (x,y)
x-2 = (1/4)(10-2)
4x-8 = 8
5x = 16
x = 4
y-4 = (1/4)(8-4)
4y-16 = 4
5y = 20
y = 5
the point is (4 , 5)
check: length between (2,4) and (4,5)
= √(2^ +1^2) = √5
length between (2,4) and (10,8)
= √(8^2 + 4^2) = √80 = 4√5
my answer is correct
Well, if you want to find the point that is one-fourth of the way from (2,4) to (10,8), we can divide the distances in both the x and y directions by 4.
First, let's find the change in the x-coordinate:
(10 - 2) = 8
Now, let's find the change in the y-coordinate:
(8 - 4) = 4
To find one-fourth of these distances, we divide them by 4:
Change in x-coordinate: 8 / 4 = 2
Change in y-coordinate: 4 / 4 = 1
Now, we can apply these changes to the starting point (2,4):
New x-coordinate: 2 + 2 = 4
New y-coordinate: 4 + 1 = 5
So, the point that is one-fourth of the way from (2,4) to (10,8) is (4,5). It's like magic, just one-fourth the magicalness!
To find the point that is one-fourth of the way from (2,4) to (10,8), we can use the following formula:
Point = (x₁ + (1/4) * (x₂ - x₁), y₁ + (1/4) * (y₂ - y₁))
Let's plug in the coordinates: (x₁, y₁) = (2, 4) and (x₂, y₂) = (10, 8).
Using the formula, we can calculate:
x-coordinate: x = 2 + (1/4) * (10 - 2) = 2 + (1/4) * 8 = 2 + 2 = 4
y-coordinate: y = 4 + (1/4) * (8 - 4) = 4 + (1/4) * 4 = 4 + 1 = 5
Therefore, the point that is one-fourth of the way from (2,4) to (10,8) is (4,5).
To find the point that is one-fourth of the way from (2,4) to (10,8), we can use the concept of finding a midpoint between two points.
Step 1: Find the difference between the x-coordinates and y-coordinates of the two given points.
Δx = 10 - 2 = 8
Δy = 8 - 4 = 4
Step 2: Multiply the differences by the desired fraction (one-fourth in this case).
Δx/4 = 8/4 = 2
Δy/4 = 4/4 = 1
Step 3: Add the calculated values to the coordinates of the starting point (2,4).
x-coordinate: 2 + 2 = 4
y-coordinate: 4 + 1 = 5
Therefore, the point that is one-fourth of the way from (2,4) to (10,8) is (4,5).