Asked by ash markens
Are the lines that goes through the points given below perpendicular? How do you know
Line 1 goes through (-5,0) and (-3,-3)
LIne 2 goes through (4,2) and (-2, -2)
Line 1 goes through (-5,0) and (-3,-3)
LIne 2 goes through (4,2) and (-2, -2)
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Answered by
GPT 3.5
To determine if the lines that go through the given points are perpendicular, we can calculate the slopes of the lines.
The slope of a line passing through points (x1, y1) and (x2, y2) can be calculated using the formula: slope = (y2 - y1) / (x2 - x1).
For Line 1, the points are (-5,0) and (-3,-3). The slope of Line 1 is: (0 - (-3)) / (-5 - (-3)) = 3 / (-2) = -1.5.
For Line 2, the points are (4,2) and (-2,-2). The slope of Line 2 is: (2 - (-2)) / (4 - (-2)) = 4 / 6 = 2 / 3.
Two lines are perpendicular to each other if the product of their slopes is -1. In this case, the product of the slopes is (-1.5) * (2 / 3) = -1. Therefore, the lines that go through the given points are perpendicular.
The slope of a line passing through points (x1, y1) and (x2, y2) can be calculated using the formula: slope = (y2 - y1) / (x2 - x1).
For Line 1, the points are (-5,0) and (-3,-3). The slope of Line 1 is: (0 - (-3)) / (-5 - (-3)) = 3 / (-2) = -1.5.
For Line 2, the points are (4,2) and (-2,-2). The slope of Line 2 is: (2 - (-2)) / (4 - (-2)) = 4 / 6 = 2 / 3.
Two lines are perpendicular to each other if the product of their slopes is -1. In this case, the product of the slopes is (-1.5) * (2 / 3) = -1. Therefore, the lines that go through the given points are perpendicular.
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