Find the distance d (P1, P2) between the points P1 and P2
P1 = (−4, 4) ; P2 = (1, 6)
wayne
distance = √( (change-in-x)^2 + (change-in-y)^2)
sub in the values
To find the distance between two points, you can use the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, P1 = (-4, 4) and P2 = (1, 6).
Substituting the values into the formula, we get:
d = √((1 - (-4))^2 + (6 - 4)^2)
Simplifying further:
d = √((5)^2 + (2)^2)
Calculating:
d = √(25 + 4)
d = √(29)
Therefore, the distance d (P1, P2) between the points P1 and P2 is √29.
To find the distance between two points, P1 and P2, you can use the distance formula. The distance formula is derived from the Pythagorean theorem and calculates the distance between two points in a 2-dimensional coordinate system.
The formula to calculate the distance, d, between two points (x1, y1) and (x2, y2) is:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Let's apply this formula to the given points P1 = (-4, 4) and P2 = (1, 6).
First, substitute the coordinates into the formula:
d = √((1 - (-4))^2 + (6 - 4)^2)
Next, simplify:
d = √((1 + 4)^2 + (2)^2)
= √(5^2 + 2^2)
= √(25 + 4)
= √29
Therefore, the distance d(P1, P2) between the points P1 = (-4, 4) and P2 = (1, 6) is √29.