Other Coordinate Geometry - SAT Subject Test in Math II
Card 0 of 2
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).
On the coordinate plane, two lines intersect at the origin. One line passes through the point
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 
.
If
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
For the second line, set
The inverse tangent of this is
making this the angle this line forms with the
Subtract:
Taking the inverse tangent:
Rounding to the nearest degree, this is
Compare your answer with the correct one above
In the figure below, regular hexagon 
has a side length of 
. Find the y-coordinate of point 
.
In the figure below, regular hexagon
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 
.
From the given information, we know that the coordinate for
Recall that the interior angle of a regular hexagon is
Since we know that this is a
Compare your answer with the correct one above