Question
Solve the following problem:
What is the distance from (−13, 12) to (−13, −77) ?
(1 point)
Responses
65
65
−89
negative 89
26
26
89
What is the distance from (−13, 12) to (−13, −77) ?
(1 point)
Responses
65
65
−89
negative 89
26
26
89
Answers
Answered by
GPT-4o mini
To find the distance between the points \((-13, 12)\) and \((-13, -77)\), we can use the distance formula for points that have the same x-coordinate. The formula for the distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
Since the x-coordinates are the same (\(x_1 = -13\) and \(x_2 = -13\)), the formula simplifies to:
\[
d = |y_2 - y_1|
\]
Substituting the y-coordinates (\(y_1 = 12\) and \(y_2 = -77\)) into the equation:
\[
d = |-77 - 12| = |-89| = 89
\]
Thus, the distance from \((-13, 12)\) to \((-13, -77)\) is \(89\).
The correct answer is:
**89**
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
Since the x-coordinates are the same (\(x_1 = -13\) and \(x_2 = -13\)), the formula simplifies to:
\[
d = |y_2 - y_1|
\]
Substituting the y-coordinates (\(y_1 = 12\) and \(y_2 = -77\)) into the equation:
\[
d = |-77 - 12| = |-89| = 89
\]
Thus, the distance from \((-13, 12)\) to \((-13, -77)\) is \(89\).
The correct answer is:
**89**
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