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Example Questions
Example Question #1 : Other Coordinate Geometry
On the coordinate plane, two lines intersect at the origin. One line passes through the point ; the other,
.
Give the measures of the acute angles they form at their intersection (nearest degree).
If is the measure of the angles that two lines with slopes
and
form, then
,
The slopes of the lines can be found by applying the slope formula
using the known points.
For the first line, set :
The inverse tangent of this is
,
making this the angle this line forms with the -axis.
For the second line, set :
The inverse tangent of this is
making this the angle this line forms with the -axis.
Subtract:
Taking the inverse tangent:
.
Rounding to the nearest degree, this is .
Example Question #11 : Coordinate Geometry
In the figure below, regular hexagon has a side length of
. Find the y-coordinate of point
.
From the given information, we know that the coordinate for must be
.
Recall that the interior angle of a regular hexagon is . Thus, we can draw in the following
triangle.
Since we know that this is a triangle, we know that the sides must be as marked, in the ratio of
. Thus, the y-coordinate of
must be
.
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All SAT II Math II Resources
