Consider the points
A(3,−3), B(−2,1), C(6,0), and D(1,4). Point A is joined to point B to create segment AB and point C is joined to point D to create segment CD.
Part A
1. What is the slope of AB?
2. What is the slope of CD?
Part B
Segments AB and CD are translated 2 units to the left to get segments A′B′ and C′D′.
1. What is the slope of A′B′?
2. What is the slope of C′D′?
Part C
1. Are the slopes the same? Explain your reasoning.
please help.
my answer is
part A
1. 4/5
2. 4/5
Part B
1. 4/5
2. 4/5
Part C
The slopes r the same.
Am I right?
Finding a slope is difference in y over difference in x. So, just find the slopes of AB and CD. Slopes remain the same after translations, so think about why that is to answer Parts B and C. When you've finished, send your answers so someone else or I could check over.
Part A:
To find the slope of a line segment, we use the formula: slope = (change in y)/(change in x).
For segment AB:
Let's consider points A(3, -3) and B(-2, 1).
Change in y = 1 - (-3) = 4
Change in x = -2 - 3 = -5
Therefore, the slope of AB = (change in y)/(change in x) = 4 / -5 = -4/5.
For segment CD:
Let's consider points C(6, 0) and D(1, 4).
Change in y = 4 - 0 = 4
Change in x = 1 - 6 = -5
Therefore, the slope of CD = (change in y)/(change in x) = 4 / -5 = -4/5.
Part B:
When segments AB and CD are translated 2 units to the left, the x-coordinate of each point is decreased by 2. Therefore, the new coordinates of the points are:
A' (3 - 2, -3) = (1, -3)
B' (-2 - 2, 1) = (-4, 1)
C' (6 - 2, 0) = (4, 0)
D' (1 - 2, 4) = (-1, 4)
To find the slopes of the translated segments, we follow the same procedure as in Part A.
For segment A'B':
Change in y = 1 - (-3) = 4
Change in x = -4 - 1 = -5
Therefore, the slope of A'B' = (change in y)/(change in x) = 4 / -5 = -4/5.
For segment C'D':
Change in y = 4 - 0 = 4
Change in x = -1 - 4 = -5
Therefore, the slope of C'D' = (change in y)/(change in x) = 4 / -5 = -4/5.
Part C:
The slopes of AB and CD are -4/5, and the slopes of A'B' and C'D' are also -4/5.
Since the slopes of the translated segments are equal to the slopes of the original segments, we can conclude that the slopes are the same.