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ISEE Lower Level Math : Lines

Study concepts, example questions & explanations for ISEE Lower Level Math

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Example Questions

Example Question #1 : Lines

There is a four sided figure in which none of the lines run parallel to each other. Which of the following could be the appropriate term to describe the figure?

Possible Answers:

Rectangle

Parallelogram

None of these

Quadrilateral

Trapezoid

Correct answer:

Quadrilateral

Explanation:

A key characteristic of a rectangle, parallelogram, and trapezoid is the fact that they each have at least one pair of lines that run parallel to each other. The only option that has lines that may not run parallel to each other is the quadrilateral, which must simply have four sides but has no specifications about parallelism.

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Example Question #1 : How To Find Symmetry

If a diagonal is drawn from one corner of a rectangle to the opposite corner, what 2 shapes result?

Possible Answers:

$2\ \textup{rectangles}$

$2\ \textup{squares}$

$2\ \textup{quadrilaterals}$

$2\ \textup{triangles}$

Correct answer:

$2\ \textup{triangles}$

Explanation:

While drawing a line across a rectangle (so that it bisects 2 sides) can result in 2 quadrilaterals, squares, or rectangles, a line drawn from one corner to the furthest corner results in two triangles. Therefore, the correct answer choice is 2 triangles.

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Example Question #2 : How To Find Symmetry

How many lines of symmetry are there in a square?

Possible Answers:

Correct answer:

Explanation:

A line of symmetry is a line that divides a polygon in half and each half is a mirror image of the other. In other words, you can fold the polygon over the symmetry line and each half matches up perfectly.

For a square there are four lines of symmetry. Two are from the diagonals of the square and two are from connecting the midpoints of the opposite sides.

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Example Question #371 : Plane Geometry

What is the distance between (2,5) and (-7, 17) ?

Possible Answers:

Correct answer:

Explanation:

The distance formula is $d=\sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}}$ .

Let $P_{1}=(-7,17)$ and $P_{2}=(2,5)$ :

$d=\sqrt{(2-(-7))^{2} + (5-17)^{2}}=\sqrt{(9)^{2} + (-12)^{2}}=\sqrt{81 + 144}=\sqrt{225}=15$

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Example Question #372 : Plane Geometry

What is the distance between (-2, 3) and (4, -5) ?

Possible Answers:

Correct answer:

Explanation:

The distance formula is given by $d=\sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}}$ .

Let $P_{1}=(4,-5)$ and $P_{2}=(-2,3)$ :

$d=\sqrt{(-2-4)^{2} + (3-(-5)^{2}}=\sqrt{(-6)^{2} + (8)^{2}}=\sqrt{36 + 64}=\sqrt{100}=10$

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Example Question #373 : Plane Geometry

What is the distance between (1,-3) and (13,-8) ?

Possible Answers:

Correct answer:

Explanation:

The distance formula is given by $d=\sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}}$ .

Let $P_{1}=(1,-3)$ and $P_{2}=(13,-8)$ :

$d=\sqrt{(13-1)^{2} + (-8-(-3)^{2}}=\sqrt{(12)^{2} + (-5)^{2}}=\sqrt{144 + 25}=\sqrt{169}=13$

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Example Question #1 : How To Find Length Of A Line

What is the distance between the points (-2,1) and (10,-4) ?

Possible Answers:

Correct answer:

Explanation:

The distance formula is $d = \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$ .

Let $P_{1}= (-2, 1)$ and $P_{2}=(10, -4)$ .

Plug these two points into the distance formula:

$d = \sqrt{(10-(-2))^{2}+(-4-1)^{2}}=\sqrt{(12)^{2}+(-5)^{2}}=\sqrt{144+25}=\sqrt{169}=13$

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Example Question #381 : Plane Geometry

If a line with a length of 5 starts at the point (1,1) , which of the following is NOT a possible end point?

Possible Answers:

(4, 5)

(-3, 4)

(5, -2)

(-2, -3)

(-3,5)

Correct answer:

(-3,5)

Explanation:

Let $P_{1}=(1,1)$ , and let $P_{2}$ be the end point we are looking for.

Recall the distance formula:

$d = \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

Squaring the distance formula gives $d^{2} = (x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}$ .

Plug $P_{1}=(1,1)$ this squared distance formula and solve for $P_{2}$ :

$25 = (x_{2}-1)^{2}+(y_{2}-1)^{2}$

Substitute each response into this equation to see which one is false. The only response that doesn't work is (-3, 5) .

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Example Question #3 : How To Find Length Of A Line

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

Possible Answers:

Correct answer:

Explanation:

The distance formula is $d = \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$ .

Let $P_{1}= (-2, 1)$ and $P_{2}=(1, 5)$ .

Plug these points into the distance formula:

$d = \sqrt{(1-(-2))^{2}+(5-1)^{2}}=\sqrt{(3)^{2}+(4)^{2}}=\sqrt{9+16}=\sqrt{25}=5$

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Example Question #6 : How To Find Length Of A Line

If a line that is 13 inches in length starts at the point (1,2) , which of the following is NOT a possible end point?

Possible Answers:

(3, 15)

(6, 14)

(-4, -10)

(-11, -3)

(13, 7)

Correct answer:

(3, 15)

Explanation:

The distance formula is given by $d = \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$ .

Square both sides:

$d^{2} = (x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}$

Now, let $P_{1}=(1,2)$ , and let $P_{2}$ be the end point we are looking for.

Plug $P_{1}=(1,2)$ into the squared distance formula and solve for $P_{2}$ :

$169 = (x_{2}-1)^{2}+(y_{2}-2)^{2}$

Alternatively, you can plug in the answer choices and see which point makes the above equation untrue. The point (3, 15) matches this description and is therefore the correct answer.

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ISEE Lower Level Math : Lines

Study concepts, example questions & explanations for ISEE Lower Level Math

All ISEE Lower Level Math Resources

Example Questions

Example Question #1 : Lines

Example Question #1 : How To Find Symmetry

Example Question #2 : How To Find Symmetry

Example Question #371 : Plane Geometry

Example Question #372 : Plane Geometry

Example Question #373 : Plane Geometry

Example Question #1 : How To Find Length Of A Line

Example Question #381 : Plane Geometry

Example Question #3 : How To Find Length Of A Line

Example Question #6 : How To Find Length Of A Line

All ISEE Lower Level Math Resources

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