Find the distance between (2,3) and (-4,-9). Round your answer to the nearest hundredth, if necessary.
Using the distance formula, we have
d = sqrt((x2-x1)^2 + (y2-y1)^2)
d = sqrt((-4-2)^2 + (-9-3)^2)
d = sqrt((-6)^2 + (-12)^2)
d = sqrt(36 + 144)
d = sqrt(180)
d ≈ 13.42
The distance between (2,3) and (-4,-9) is approximately 13.42.
To find the distance between two points in a plane, we can use the distance formula.
The distance formula is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Let's substitute the given coordinates into the formula:
d = sqrt((-4 - 2)^2 + (-9 - 3)^2)
Simplifying further:
d = sqrt((-6)^2 + (-12)^2)
= sqrt(36 + 144)
= sqrt(180)
To round the answer to the nearest hundredth, we evaluate:
sqrt(180) ≈ 13.42
Therefore, the distance between the points (2,3) and (-4,-9) is approximately 13.42.
To find the distance between two points on a coordinate plane, you can use the formula for the distance between two points, also known as the distance formula.
The distance formula is derived from the Pythagorean theorem, and it states that the distance between two points (x1, y1) and (x2, y2) is equal to the square root of the sum of the squares of the differences of the x-coordinates and the y-coordinates. In mathematical notation, this can be written as:
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Using this formula, we can find the distance between the points (2,3) and (-4,-9).
Let's label the first point as (x1, y1) = (2, 3) and the second point as (x2, y2) = (-4, -9).
Now, substituting the values into the distance formula, we get:
Distance = √[(-4 - 2)^2 + (-9 - 3)^2]
Simplifying further:
Distance = √[(-6)^2 + (-12)^2]
Distance = √[36 + 144]
Distance = √180
Rounding the answer to the nearest hundredth, we get:
Distance = 13.42
Therefore, the distance between the points (2,3) and (-4,-9) is approximately 13.42 units.