SAT II Math II : Coordinate Geometry

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

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Example Questions

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Example Question #135 : Geometry

Axes_1

Refer to the above figure.

Which of the following functions is graphed?

Possible Answers:

Correct answer:

Explanation:

Below is the graph of :

Axes_1

If the graph of  is translated by shifting each point  to the point , the graph of

 

is formed. If the graph is then shifted down by four units, the new graph is

.

Since the starting graph was , the final graph is

, or

Example Question #1 : Transformations

Axes_1

Refer to the above figure.

Which of the following functions is graphed?

Possible Answers:

Correct answer:

Explanation:

Below is the graph of :

Axes_1

If the graph of  is translated by shifting each point  to the point , the graph of

 

is formed. If the graph is then shifted right by two units, the new graph is

Since the starting graph was , the final graph is

, or

Example Question #1 : Distance Formula

What is the distance between the point (1,2) and (8,5)?

Possible Answers:

Correct answer:

Explanation:

For this question we will use the distance formula to solve.

In our case  

and 

Substituting these values in we get the following

Example Question #441 : Sat Subject Test In Math Ii

The points A=(-2,0), B=(0,3), and C=(0,0) makes a triangle.  What is the distance between point A and point B?

Possible Answers:

Correct answer:

Explanation:

For this question we need to use the distance formula for points A and B.

Point A will be our  and point B will be 

Now we substitute these values into the following:

Example Question #11 : Coordinate Geometry

Find the distance between the two points (2,7) and (4,6).

Possible Answers:

Correct answer:

Explanation:

The distance between two points is found using the formula 

For this problem the values are as follows:

Input the values into the formula and simplify

Example Question #1 : Midpoint Formula

Find the point halfway between points A and B.

Possible Answers:

Correct answer:

Explanation:

Find the point halfway between points A and B.

We are going to need to use midpoint formula. If you ever have difficulty recalling midpoint formula, try to recall that it is basically taking two averages. One average is the average of your x values, the other average is the average of your y values.

Now we plug and chug!

So our answer is (43,44)

Example Question #11 : Coordinate Geometry

What is the coordinates of the point exactly half way between (-2, -3) and (5, 7)?

Possible Answers:

Correct answer:

Explanation:

We need to use the midpoint formula to solve this question.

In our case 

and 

Therefore, substituting these values in we get the following:

Example Question #1 : Midpoint Formula

Find the midpoint between  and .

Possible Answers:

Correct answer:

Explanation:

Write the midpoint formula.

Substitute the points.

The answer is:  

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:

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 #12 : 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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