Difference between revisions of "2017 AMC 10B Problems/Problem 10"
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Latest revision as of 17:50, 17 January 2021
Contents
[hide]Problem
The lines with equations and
are perpendicular and intersect at
. What is
?
Solution
Writing each equation in slope-intercept form, we get and
. We observe the slope of each equation is
and
, respectively. Because the slope of a line perpendicular to a line with slope
is
, we see that
because it is given that the two lines are perpendicular. This equation simplifies to
.
Because is a solution of both equations, we deduce
and
. Because we know that
, the equations reduce to
and
. Solving this system of equations, we get
Video Solution
~savannahsolver
Video Solution by TheBeautyofMath
https://youtu.be/XRfOULUmWbY?t=582
~IceMatrix
See Also
2017 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 9 |
Followed by Problem 11 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.