### All SAT II Math II Resources

## Example Questions

### Example Question #12 : 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).

**Possible Answers:**

**Correct answer:**

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 #1 : Other Coordinate Geometry

In the figure below, regular hexagon has a side length of . Find the y-coordinate of point .

**Possible Answers:**

**Correct answer:**

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 .