2017 AMC 10B Problems/Problem 8
Contents
Problem
Points and
are vertices of
with
. The altitude from
meets the opposite side at
. What are the coordinates of point
?
Solution 1
Since , then
is isosceles, so
. Therefore, the coordinates of
are
.
Solution 2
Calculating the equation of the line running between points and
,
. The only coordinate of
that is also on this line is
.
Solution 3
Similar to the first solution, because the triangle is isosceles, then the line drawn in the middle separates the triangle into two smaller congruent triangles. To get from to
, we go to the right
and up
. Then to get to point
from point
, we go to the right
and up
, getting us the coordinates
. ~
Video Solution
~savannahsolver
Video Solution by TheBeautyofMath
https://youtu.be/XRfOULUmWbY?t=367
~IceMatrix
See Also
2017 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 7 |
Followed by Problem 9 | |
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 |
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