ISEE Middle Level Quantitative : Geometry

Study concepts, example questions & explanations for ISEE Middle Level Quantitative

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Example Questions

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Example Question #1 : How To Find A Line On A Coordinate Plane

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

Possible Answers:

Correct answer:

Explanation:

Use the point-slope formula with 

Example Question #2 : How To Find A Line On A Coordinate Plane

Which is the greater quantity?

(A) The slope of the line 

(B) The slope of the line 

Possible Answers:

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

(B) is greater

(A) is greater

(A) and (B) are equal

Correct answer:

(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 #1 : How To Find A Line On A Coordinate Plane

Which is the greater quantity?

(A) The slope of the line 

(B) The slope of the line 

Possible Answers:

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

(B) is greater

(A) is greater

(A) and (B) are equal

Correct answer:

(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 #1 : 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 .

Possible Answers:

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

(a) is the greater quantity

(a) and (b) are equal

(b) is the greater quantity

Correct answer:

(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 #2 : Coordinate Geometry

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

Possible Answers:

Undefined

Correct answer:

Explanation:

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

:

in the slope formula:

Example Question #1 : How To Find The Points On A Coordinate Plane

Choose the best answer from the four choices given.

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

Possible Answers:

Correct answer:

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 #2 : Geometry

Choose the best answer from the four choices given.

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

Possible Answers:

Correct answer:

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 #1 : Geometry

Choose the best answer from the four choices given.

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

Possible Answers:

Correct answer:

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 #1 : Geometry

The ordered pair is in which quadrant?

Possible Answers:

Quadrant V

Quadrant II

Quadrant IV

Quadrant III

Quadrant I

Correct answer:

Quadrant II

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 #3 : Geometry

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

Possible Answers:

Obtuse

Complementary

Acute

Supplementary. 

Correct answer:

Supplementary. 

Explanation:

Two angles that are supplementary add up to 180 degrees. They cannot both be acute, nor can they both be obtuse. Therefore, "Supplementary" is the correct answer. 

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