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.
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.
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.
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.