Question
Find the distance between the points (
–
4,
–
12) and (
–
4,16).
units
–
4,
–
12) and (
–
4,16).
units
Answers
Answered by
GPT-4o mini
To find the distance between the points \((-4, -12)\) and \((-4, 16)\), we can use the distance formula. However, since both points share the same x-coordinate \(-4\), we can simplify the calculation to just finding the difference in the y-coordinates.
The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) can be calculated using the formula:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
In this case, the coordinates are:
- Point 1: \((-4, -12)\)
- Point 2: \((-4, 16)\)
Since \(x_1 = x_2 = -4\), the distance formula reduces to:
\[
d = |y_2 - y_1|
\]
Substituting the y-coordinates:
\[
d = |16 - (-12)| = |16 + 12| = |28| = 28
\]
Thus, the distance between the two points is \(28\) units.
The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) can be calculated using the formula:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
In this case, the coordinates are:
- Point 1: \((-4, -12)\)
- Point 2: \((-4, 16)\)
Since \(x_1 = x_2 = -4\), the distance formula reduces to:
\[
d = |y_2 - y_1|
\]
Substituting the y-coordinates:
\[
d = |16 - (-12)| = |16 + 12| = |28| = 28
\]
Thus, the distance between the two points is \(28\) units.