If point C has coordinated (4,2) and point D has coordinates (8,5) then what is the length of CD?
For any two points (a,b) and (c,d) the distance between them is found by
√[ (a-c)^2 + (b-d)^2 ]
plug in your numbers
To find the length of CD, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, CD is the hypotenuse, and the other two sides are the horizontal distance (x-coordinate) and the vertical distance (y-coordinate) between the two points.
So, we first find the horizontal distance:
Horizontal distance = Difference in x-coordinates = 8 - 4 = 4
Next, we find the vertical distance:
Vertical distance = Difference in y-coordinates = 5 - 2 = 3
Now, using the Pythagorean theorem:
Length of CD = √(Horizontal distance^2 + Vertical distance^2)
= √(4^2 + 3^2)
= √(16 + 9)
= √25
= 5
Therefore, the length of CD is 5 units.
To find the length of CD, you can use the distance formula, which is based on the Pythagorean theorem. The distance formula is:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Here, (x1, y1) represents the coordinates of point C, and (x2, y2) represents the coordinates of point D. Let's substitute these values into the formula:
Distance = √((8 - 4)^2 + (5 - 2)^2)
Distance = √(4^2 + 3^2)
Distance = √(16 + 9)
Distance = √25
Distance = 5
Therefore, the length of CD is 5 units.