# SAT II Math II : Other Coordinate Geometry

## Example Questions

### Example Question #143 : 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).      Explanation:

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 #144 : Geometry

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