SAT II Math II : Other Coordinate Geometry

Study concepts, example questions & explanations for SAT II Math II

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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).

Possible Answers:

Correct answer:

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 #20 : Coordinate Geometry

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

1

Possible Answers:

Correct answer:

Explanation:

1

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.

13

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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