Find the distance between (2, 3) and (−4, −9) . Round your answer to the nearest hundredth, if necessary.(1 point
To find the distance between two points (x1, y1) and (x2, y2), you can use the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, the coordinates of the first point are (x1, y1) = (2, 3) and the coordinates of the second point are (x2, y2) = (-4, -9).
Plugging these values into the distance formula, we get:
Distance = √((-4 - 2)^2 + (-9 - 3)^2)
Calculating this expression, we have:
Distance = √((-6)^2 + (-12)^2)
Distance = √(36 + 144)
Distance = √180
Rounding this to the nearest hundredth, we get:
Distance ≈ 13.42
Therefore, the distance between (2, 3) and (-4, -9) is approximately 13.42 units.
To find the distance between two points, we can use the distance formula, which is derived from the Pythagorean theorem.
The distance formula states that the distance between two points (x1, y1) and (x2, y2) in a coordinate plane is given by the formula:
distance = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, the coordinates of the two points are (2, 3) and (-4, -9). Let's plug these values into the distance formula:
distance = √((-4 - 2)^2 + (-9 - 3)^2)
Simplifying the formula, we have:
distance = √((-6)^2 + (-12)^2)
distance = √(36 + 144)
distance = √(180)
Now, to find the distance to the nearest hundredth, we need to find the approximate square root of 180. Approximating, we get:
distance ≈ 13.42 (rounded to the nearest hundredth)
Therefore, the distance between the points (2, 3) and (-4, -9) is approximately 13.42 units.
Using the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the given values:
d = sqrt((-4 - 2)^2 + (-9 - 3)^2)
d = sqrt((-6)^2 + (-12)^2)
d = sqrt(36 + 144)
d = sqrt(180)
The distance between (2, 3) and (-4, -9) is approximately 13.42.