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Straight line L, is perpendicular to straight line L, that goes

through points (3, 7) and (5, 12)
L, passes through points (0, 13) and (x, 21)
Work out the value of x.
Optional working
x = Answ
+

User Simianarmy
by
8.4k points

1 Answer

2 votes
To find the value of x, we first need to find the equation of the line L that goes through the points (3, 7) and (5, 12).
The slope of this line is:
m = (y2 - y1) / (x2 - x1) = (12 - 7) / (5 - 3) = 5/2
We can use the point-slope form of the equation of a line to find the equation of L:
y - y1 = m(x - x1)
Using the point (3, 7):
y - 7 = (5/2)(x - 3)
Simplifying:
y = (5/2)x - (1/2)
Since L is perpendicular to this line, its slope is the negative reciprocal of 5/2:
m' = -2/5
Using the point-slope form of the equation of a line again, we can find the equation of L:
y - 13 = (-2/5)(x - 0)
Simplifying:
y = (-2/5)x + 13
To find the value of x when this line passes through (x, 21), we can substitute y = 21 into the equation:
21 = (-2/5)x + 13
Solving for x:
x = (21 - 13) / (-2/5) = -4.375
Therefore, the value of x is approximately -4.375.
User Avisheks
by
7.5k points
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