What is the distance, in units, between the points (2, -6) and (-4, 3)? Express your answer in simplest radical form.
3 sqrt(13)
Well, let's find out! To calculate the distance between two points (x₁, y₁) and (x₂, y₂), we can use the distance formula, which is the square root of the sum of the squares of the differences in x and y coordinates. In this case, the distance would be:
√((x₂ - x₁)² + (y₂ - y₁)²)
Plugging in the values from the question, we have:
√((-4 - 2)² + (3 - (-6))²)
Simplifying further:
√((-6)² + (3 + 6)²)
√(36 + 81)
√117
So, the distance between the points (2, -6) and (-4, 3) is √117 units. However, I'm not sure if you'll find that quite "radical" enough for your liking! Keep it fun!
To find the distance between two points in a plane, we can use the distance formula. The distance formula states that the distance between two points (x1, y1) and (x2, y2) is given by the square root of the sum of the squares of the differences of the x-coordinates and y-coordinates.
Let's calculate the distance between the points (2, -6) and (-4, 3) using the distance formula:
Step 1: Identify the coordinates of the two points.
- The first point is (2, -6).
- The second point is (-4, 3).
Step 2: Apply the distance formula.
The distance formula is:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the values:
d = √((-4 - 2)^2 + (3 - (-6))^2)
Simplifying:
d = √((-6)^2 + (3 + 6)^2)
= √(36 + 81)
= √117
Therefore, the distance between the points (2, -6) and (-4, 3) is √117 units in simplest radical form.
use your distance formula
√((-4-2)^2 + (3+6)^2) = √(6^2+9^2) = ____