What is the distance between the points (-4,2) and (-9,-10)?
The distance between two points can be calculated using the distance formula: \( \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)
Given points: \( P_1(-4,2) \) and \( P_2(-9,-10) \)
Let's calculate the distance:
\( x_2 - x_1 = -9 - (-4) = -9 + 4 = -5 \)
\( y_2 - y_1 = -10 - 2 = -12 \)
Now, substitute the values into the formula:
\( \sqrt{(-5)^2 + (-12)^2} = \sqrt{25 + 144} = \sqrt{169} \)
Therefore, the distance between the points (-4,2) and (-9,-10) is 13.
Explanation:
The distance between two points in a coordinate plane can be found using the distance formula which is derived from the Pythagorean theorem. The formula allows us to calculate the length of the line segment that connects two points.
In this case, the given points are (-4,2) and (-9,-10). To find the distance between them, we first calculate the difference in x-coordinates and y-coordinates. By subtracting the x-coordinates and y-coordinates of the two points, we get the values -5 and -12 respectively.
Next, we apply these values to the distance formula: \( \sqrt{(-5)^2 + (-12)^2} \). This simplifies to \( \sqrt{25 + 144} \) which further simplifies to \( \sqrt{169} \).
Therefore, the distance between the points (-4,2) and (-9,-10) is 13 units.