# ISEE Middle Level Quantitative : Coordinate Geometry

## Example Questions

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### Example Question #1 : Geometry

Give the equation of the line through point  that has slope .

Explanation:

Use the point-slope formula with

### Example Question #2 : Coordinate Geometry

Which is the greater quantity?

(A) The slope of the line

(B) The slope of the line

(A) is greater

(A) and (B) are equal

(B) is greater

It is impossible to determine which is greater from the information given

(A) is greater

Explanation:

Rewrite each in the slope-intercept form,  will be the slope.

The slope of this line is .

The slope of this line is .

Since , (A) is greater.

### Example Question #3 : Coordinate Geometry

Which is the greater quantity?

(A) The slope of the line

(B) The slope of the line

(A) and (B) are equal

It is impossible to determine which is greater from the information given

(B) is greater

(A) is greater

(A) and (B) are equal

Explanation:

Rewrite each in the slope-intercept form,  will be the slope.

The slope of the line of  is

The slope of the line of  is also

The slopes are equal.

### Example Question #4 : Coordinate Geometry

and  are positive integers, and . Which is the greater quantity?

(a) The slope of the line on the coordinate plane through the points  and .

(b) The slope of the line on the coordinate plane through the points  and .

(a) and (b) are equal

(a) is the greater quantity

It is impossible to determine which is greater from the information given

(b) is the greater quantity

(a) and (b) are equal

Explanation:

The slope of a line through the points  and  can be found by setting

in the slope formula:

The slope of a line through the points  and  can be found similarly:

The lines have the same slope.

### Example Question #5 : Coordinate Geometry

A line passes through the points with coordinates  and , where . Which expression is equal to the slope of the line?

Undefined

Explanation:

The slope of a line through the points  and , can be found by setting

:

in the slope formula:

### Example Question #6 : Coordinate Geometry

Choose the best answer from the four choices given.

The point (15, 6) is on which of the following lines?

Explanation:

For this problem, simply plug in the values for the point (15,6) into the different equations (15 for the -value and 6 for the -value) to see which one fits.

(NO)

(YES!)

(NO)

(NO)

### Example Question #7 : Coordinate Geometry

Choose the best answer from the four choices given.

What is the point of intersection for the following two lines?

Explanation:

At the intersection point of the two lines the - and - values for each equation will be the same. Thus, we can set the two equations as equal to each other:

point of intersection

### Example Question #8 : Coordinate Geometry

Choose the best answer from the four choices given.

What is the -intercept of the line represented by the equation

Explanation:

In the formula , the y-intercept is represented by (because if you set to zero, you are left with ).

Thus, to find the -intercept, set the value to zero and solve for .

### Example Question #9 : Coordinate Geometry

The ordered pair is in which quadrant?

Explanation:

There are four quadrants in the coordinate plane. Quadrant I is the top right, and they are numbered counter-clockwise. Since the x-coordinate is , you go to the left one unit (starting from the origin). Since the y-coordinate is , you go upwards four units. Therefore, you are in Quadrant II.

### Example Question #10 : Coordinate Geometry

If angles s and r add up to 180 degrees, which of the following best describes them?

Complementary

Obtuse

Acute

Supplementary.