Find the distance between (2, 3) and (-4, -9). Round your answer to the nearest hundredth, if necessary.
__ units
To find the distance between two points (x1, y1) and (x2, y2), you can use the distance formula:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
So, the distance between (2, 3) and (-4, -9) is:
distance = sqrt((-4 - 2)^2 + (-9 - 3)^2)
distance = sqrt((-6)^2 + (-12)^2)
distance = sqrt(36 + 144)
distance = sqrt(180)
distance ≈ 13.42 units
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 states:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Given that the coordinates of the two points are (2, 3) and (-4, -9), we can substitute these values into the formula:
Distance = √((-4 - 2)^2 + (-9 - 3)^2)
Simplifying this equation gives:
Distance = √((-6)^2 + (-12)^2)
Distance = √(36 + 144)
Distance = √180
To round the answer to the nearest hundredth, we can use a calculator:
Distance ≈ 13.42 units
Therefore, the distance between (2, 3) and (-4, -9) is approximately 13.42 units.
To find the distance between two points in a coordinate plane, you can use the distance formula. The distance formula states that the distance between two points (x1, y1) and (x2, y2) can be calculated as:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, the coordinates of the two points are (2, 3) and (-4, -9). By substitution, we have:
distance = sqrt((-4 - 2)^2 + (-9 - 3)^2)
= sqrt((-6)^2 + (-12)^2)
= sqrt(36 + 144)
= sqrt(180)
To simplify the square root, we can factor out 36:
sqrt(180) = sqrt(36 * 5)
= sqrt(36) * sqrt(5)
= 6 * sqrt(5)
So, the distance between (2, 3) and (-4, -9) is 6 * sqrt(5) units.
Rounding to the nearest hundredth, the distance is approximately 13.42 units.