How to find symmetry - ISEE Lower Level Quantitative Reasoning

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Question

is the midpoint of the number line that extends from to . What is the value of ?

Answer

Find the average of the two endpoints to find their midpoint. To find the average of two numbers, add them together and divide by two.

$\frac{-3 + 7}{2} = \frac{4}{2} = 2$

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Question

The length of a certain line is inches. If this line is cut in half, how long is each half?

Answer

Divide the length of the line by 2 to find the length of each half:

$46\div 2=23\ inches$

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Question

How many lines of symmetry does a square have?

Answer

A line of symmetry is the imaginary line that you draw through a shape so that you can fold the image over the line and have both halves match exactly. Any regular shape has as many lines of symmetry as it does sides. Since a square has four sides, the correct answer is 4!

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Question

How many lines of symmetry does an octagon have?

Answer

A line of symmetry divides a shape into two equal and identical halves. Any regular shape has as many lines of symmetry as it does sides. Since octagons have eight sides, the correct answer is 8.

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Question

How many lines of symmetry does a rectangle have?

Answer

A line of symmetry is the imaginary line that you draw through a shape so that you can fold the image over the line and have both halves match exactly. Any regular shape has as many lines of symmetry as it does total sides. Since a rectangle has four sides, the correct answer is 4!

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Question

How many lines of symmetry does an octagon have?

Answer

A line of symmetry is the imaginary line that you draw through a shape so that you can fold the image over the line and have both halves match exactly. Any regular shape has as many lines of symmetry as it does sides. Since an octagon has eight sides, the correct answer is .

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Question

Ms. Johnson is knitting a blanket for her grandson. She has a piece of yarn that is exactly feet long however, she only needs half of the piece of yarn. What is the length of the piece of yarn that Ms. Johnson needs to make the blanket for her grandson?

Answer

Ms. Johnson started with feet of yarn, however she only needs half of the feet.

To find the length of the amount of yarn that she needs, divide in half.

The solution is:

$\frac{5}{2}=2.5$

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Question

Mr. Thomas' rectangular garden has a width of feet. The length of his garden is exactly half the distance of the width of the garden. How long is the length of Mr. Thomas' garden?

Answer

The length of Mr. Thomas' garden is exactly half the distance of the width of the garden.

The width of the garden is feet.

Thus, the length is equal to,

$\frac{32}{2}=16$

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Question

Celeste is Debra's year old daughter. Both Debra and Celeste measured their height on the wall. Celeste was surprised to find out that she is exactly half the height of her mother. If Debra is $5 \tfrac{1}{2}$ feet tall, how tall is Celeste?

Answer

Debra is $5\tfrac{1}{2}$ feet tall. Celeste is half the height of her mother Debra.

Thus, to find Celeste's height, divide $5\tfrac{1}{2}$ in half.

The solution is:

Step one: convert $5\tfrac{1}{2}$ into an improper fraction.

$5\tfrac{1}{2}=\frac{11}{2}$

Step two: divide $\frac{11}{2}$ by .

$\frac{\frac{11}{2}}{2}=\frac{11}{2}\cdot\frac{1}{2}=\frac{11}{4}$

Step three: express $\frac{11}{4}$ in feet as a mixed number.

$11\div4=2\tfrac{3}{4}$

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Question

Mr. Lam is planning on painting a rectangular wall in his living room. Before he starts painting, he decided to take a few measurements of the wall. He finds out that the width of the wall is twice the measurement of the height of the wall. If the width of the wall is feet, what is the height of the wall?

Answer

Since the height of the rectangular wall is half the length of the width, divide by

The solution is:

$25 \div2=12\tfrac{1}{2}$

Check:

$12\times2=24$
$2\times \frac{1}{2}=1$

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Question

The cable on Ryan's new cellphone charger is twice as long as his old cellphone charger cable. If Ryan's new cellphone charger has a feet long cable, how long was his old charger cable?

Answer

To find the length of Ryan's old cellphone cable, divide the length of his new cellphone charger in half.

The solution is:

$\small 3\div2=1\tfrac{1}{2}$

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Question

Line segment $\small \bar{AE}$ is twice as long as line segment $\small \bar{AC}$ . If line segment $\small \bar{AE}$ is inches, how many inches is $\small \bar{AC}$ ?

Answer

The length of line segment $\small \bar{AC}$ is half the length of line segment $\small \bar{AE}$ .

Therefore, divide $\small 56$ by $\small 2$ .

$\small 56 \div2=28$

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Question

Line segment $\small \bar{JK}$ is twice as long as line segment $\small \bar{LP}$ . If line segment $\small \bar{JK}$ is $\small 148$ centimeters, how many centimeters is line segment $\small \bar{LP}$ ?

Answer

To find the length of line segment $\small \bar{LP}$ , divide the length of line segment $\small \bar{JK}$ .
Therefore, the length of line segment $\small \bar{LP}$ is:

$\small 148 \div 2=74$

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Question

Find the midpoint between coordinate points $\small (-2,4)$ and $\small \small (4,4)$ .

Answer

To find the midpoint between these two coordinate points, use the formula,

$\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} \right )$

Since our and our the midpoint formula becomes,

$\left(\frac{-2+4}{2},\frac{4+4}{2}\right )=\left(\frac{2}{2}, \frac{8}{2} \right )=(1,4)$ .

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Question

Line segment $\small \bar{xy}$ is twice as long as line segment $\small \bar{ab}$ and half as long as line segment $\small \bar{cd}$ . If line segment $\small \bar{cd}$ is $\small 84$ meters, how long is line segment $\small \bar{xy}$ ?

Answer

Since line segment $\small \bar{xy}$ is half the length of line segment $\small \bar{cd}$ we need to divide $\small 84$ by $\small 2$ .

$\small 84\div2=42$

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Question

In a football contest, Jeff threw the football twice as far as Robby. If Jeff threw the ball $\small 38$ yards, how many yards did Robby throw the ball?

Answer

Since Jeff threw the football twice as far as Robby, divide $\small 38$ by $\small 2$ .

$\small 38\div2=19$

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Question

Line segment $\small \bar{xy}$ goes exactly halfway across a sheet of paper. If the sheet of paper has a width of $\small 12\tfrac{1}{2}$ inches, how long is line segment $\small \bar{xy}$ ?

Answer

Since the length of line segment $\small \bar{xy}$ is half of $\small 12\tfrac{1}{2}$ , convert $\small 12\tfrac{1}{2}$ to a mixed number.

$\small 12\tfrac{1}{2}= \frac{12 \cdot 2 +1}{2}= \frac{25}{2}$

Then divide $\small \frac{25}{2}$ by .

$\small \frac{25}{2}\div2=\frac{25}{2}\times \frac{1}{2}=\frac{25}{4}$

Then convert $\small \frac{25}{4}$ to a mixed number.

$\small \frac{25}{4}=6\tfrac{1}{4}$

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Question

The Johnson family had an extension put onto their driveway that doubled the width of the driveway. If their driveway was originally $\small 13$ feet wide, how wide is their new driveway?

Answer

Since the original driveway was half the width of the new driveway, multiply $\small 13$ by $\small 2$ .

$\small 13\times2=26$

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Question

Does the black line in the figure represent a line of symmetry?

Answer

When you are trying to decide if a line represents a line of symmetry you can think about folding the figure across that line. Once you make the fold, do all of the parts line up on top?

If yes, then the line represents a line of symmetry.

If no, then the line does not represent a line of symmetry.

This line represents a line of symmetry because if you fold on the black line, then one side would lay on top of the other and the parts would match up.

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Question

Does the black line in the figure represent a line of symmetry?

Answer

When you are trying to decide if a line represents a line of symmetry you can think about folding the figure across that line. Once you make the fold, do all of the parts line up on top?

If yes, then the line represents a line of symmetry.

If no, then the line does not represent a line of symmetry.

This line does not represents a line of symmetry because if you fold on the black line, one side will not lay on top of the other with parts that match up.

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