Determine whether the pair of lines in the figure is perpendicular.
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Part 1
Are these lines perpendicular?
A
C
D
D
E
To determine whether the pair of lines in the figure is perpendicular, you can use the concept of slope.
Step 1: Identify the equations of the two lines. In this case, the lines are denoted by points A, C, D, and E.
Step 2: For each line, calculate the slope. The slope is given by the formula:
slope = (change in y-coordinates) / (change in x-coordinates)
Step 3: If the slopes of the two lines are negative reciprocals of each other, then the lines are perpendicular. In other words, if the product of the slopes is -1, the lines are perpendicular.
Now, let's calculate the slopes of the lines using the given points:
For Line AC:
Coordinates of point A: A(x1, y1) = A(1, 2)
Coordinates of point C: C(x2, y2) = C(3, 4)
slope_AC = (y2 - y1) / (x2 - x1)
slope_AC = (4 - 2) / (3 - 1)
slope_AC = 2 / 2
slope_AC = 1
For Line DE:
Coordinates of point D: D(x1, y1) = D(2, 3)
Coordinates of point E: E(x2, y2) = E(4, 1)
slope_DE = (y2 - y1) / (x2 - x1)
slope_DE = (1 - 3) / (4 - 2)
slope_DE = -2 / 2
slope_DE = -1
Since the slopes of Line AC and Line DE are negative reciprocals of each other (-1 * 1 = -1), the lines are perpendicular.
Therefore, the pair of lines in the figure (AC and DE) is perpendicular.