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(3,2)\ | /
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In the accompanying figure, the slope of line k is t and the slpe of line m is negative t. What is the value of s?
(the lines are perpendicular)
(sorry for the ascii graph ^_^)
(I have a test tomorrow)
(help)
To find the value of s, we need to use the given information about the slopes of the lines.
The slope of a line is given by the formula: slope = (y2 - y1) / (x2 - x1)
Let's consider line k with slope t. We know that the points (3, 2) and (s, 1) lie on this line. So we can plug in the coordinates into the slope formula:
t = (1 - 2) / (s - 3)
t = -1 / (s - 3)
Now, let's consider line m with slope negative t. We know that the points (3, 2) and (s, 1) lie on this line as well. So we can plug in the coordinates into the slope formula:
-negative t = (1 - 2) / (s - 3)
t = -2 + 3 / (s - 3)
t = 1 / (s - 3)
Since we know that the slopes of the two lines are equal in magnitude but opposite in sign, we can set up an equation:
-t = t
-1 / (s - 3) = -1 / (s - 3)
Cross-multiplying, we get:
(s - 3) = -(s - 3)
s - 3 = -s + 3
Adding s to both sides:
2s - 3 = 3
Adding 3 to both sides:
2s = 6
Dividing by 2:
s = 3
Therefore, the value of s is 3.