Which of the following options is a real-world example of a plane?

Question

Option #1: a location on a map

Option #2: a room in a house

Option #3: a countertop

(1 point)
Option #
is a real-world example of a plane.

Answer 1

Option #3: a countertop is a real-world example of a plane.

In geometry, a plane is defined as a flat, two-dimensional surface that extends infinitely in all directions. A countertop provides a practical, tangible example of this concept as it is flat and can be considered two-dimensional within the bounds of a kitchen or workspace.

Answer 2

Liam is planning to construct a line segment bisector of AB¯¯¯¯¯¯¯¯ . He plans to use the following steps:

Step #1: Create line segment AB¯¯¯¯¯¯¯¯ on my paper.

Step #2: Fold the paper so that point A is on top of point B .

Step #3: Unfold the paper and label the intersection of the fold and the line segment with point C .

Step #4: Use a straight edge to draw a line that passes through points A , C , and B . This line is a bisector of AB¯¯¯¯¯¯¯¯ .

Which step has a mistake and how should the mistake be corrected?

(1 point)
Responses

Step #4 has a mistake. It should say: “Use a straight edge to draw a line that passes through point C (but not points A and B). This line is a bisector of AB¯¯¯¯¯¯¯¯.”
Step #4 has a mistake. It should say: “Use a straight edge to draw a line that passes through point upper C (but not points upper A and upper B ). This line is a bisector of Modifying above upper A upper B with bar .”

Step #2 has a mistake. It should say: “Fold the paper so that point A is on top of point B. Then, fold the paper again so that the midpoint of AB¯¯¯¯¯¯¯¯ is on top of points A and B .”
Step #2 has a mistake. It should say: “Fold the paper so that point upper A is on top of point upper B . Then, fold the paper again so that the midpoint of Modifying above upper A upper B with bar is on top of points upper A and upper B .”

Step #4 has a mistake. It should say: “Use a straight edge to draw a line that passes through point A and another line that passes through point B. These lines are bisectors of AB¯¯¯¯¯¯¯¯.”
Step #4 has a mistake. It should say: “Use a straight edge to draw a line that passes through point upper A and another line that passes through point upper B . These lines are bisectors of Modifying above upper A upper B with bar .”

Step #2 has a mistake. It should say: “Fold the paper along line segment AB¯¯¯¯¯¯¯¯.”

Answer 3

The mistake is in Step #4. The correct option is:

Step #4 has a mistake. It should say: “Use a straight edge to draw a line that passes through point C (but not points A and B). This line is a bisector of AB¯¯¯¯¯¯¯¯.”

In this step, the bisector of line segment AB should only be the line that passes through point C, which is the midpoint, rather than drawing a line that goes through points A and B as well.

Answer 4

Which set of side lengths will form a triangle? All measurements are in feet.(1 point)
Responses

4, 1, 6
4, 1, 6

8, 6, 2
8, 6, 2

3, 3, 6
3, 3, 6

5, 2, 4

Answer 5

To determine if a set of side lengths can form a triangle, we can use the triangle inequality theorem. This theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Let's evaluate each set of side lengths:

1. 4, 1, 6

   • 4 + 1 > 6: No (5 is not greater than 6)
   • 4 + 6 > 1: Yes
   • 1 + 6 > 4: Yes
   • This set cannot form a triangle.

2. 8, 6, 2

   • 8 + 6 > 2: Yes
   • 8 + 2 > 6: Yes
   • 6 + 2 > 8: No (8 is not greater than 8)
   • This set cannot form a triangle.

3. 3, 3, 6

   • 3 + 3 > 6: No (6 is not greater than 6)
   • 3 + 6 > 3: Yes
   • 3 + 6 > 3: Yes
   • This set cannot form a triangle.

4. 5, 2, 4

   • 5 + 2 > 4: Yes
   • 5 + 4 > 2: Yes
   • 2 + 4 > 5: Yes
   • This set can form a triangle.

Therefore, the side lengths 5, 2, 4 will form a triangle.

Answer 6

The line y=−x+1 is drawn on the coordinate plane. It is translated 1 unit to the right and 2 units up. What is the equation of the translated line?(1 point)
Responses

y=x+3
y equals x plus 3

y=−x+4
y equals negative x plus 4

y=3
y equals 3

y=x+4

Answer 7

To find the equation of the translated line, we start with the original equation:

\[ y = -x + 1 \]

Step 1: Translate 1 unit to the right.

Translating a line 1 unit to the right means replacing every \( x \) in the equation with \( x - 1 \):

\[ y = - (x - 1) + 1 \] \[ y = -x + 1 + 1 \] \[ y = -x + 2 \]

Step 2: Translate 2 units up.

Translating a line 2 units up means adding 2 to the entire equation:

\[ y = -x + 2 + 2 \] \[ y = -x + 4 \]

Thus, the equation of the translated line is:

\[ \boxed{y = -x + 4} \]

So the correct response is y = -x + 4.

Answer 8

A point is translated on the coordinate plane from (4,−1) to (6,−1) .Which function shows this translation?(1 point)
Responses

f(x)=x−2
f left parenthesis x right parenthesis equals x minus 2

f(x)=x+5
f left parenthesis x right parenthesis equals x plus 5

f(x)=x+2
f left parenthesis x right parenthesis equals x plus 2

f(x)=x
f left parenthesis x right parenthesis equals x

Answer 9

To determine the function that shows this translation, we need to identify how the point \((4, -1)\) moves to the point \((6, -1)\).

Analyzing the Translation

• The x-coordinate changes from \(4\) to \(6\), which is an increase of \(2\).
• The y-coordinate remains constant at \(-1\).

In terms of a function describing this translation, we only need to modify the x-coordinate by adding \(2\).

Function Representation

The function that represents this translation can be defined as:

\[ f(x) = x + 2 \]

This function takes an input \(x\), adds \(2\) to it, which is exactly the translation we see in the given point.

Conclusion

Thus, the correct answer is:

f(x) = x + 2.

Answer 10

A triangle has vertices W(−3,7) , Q(1,−1) , and Z(−5,−2) . Apply rotation mapping rules to find the coordinates of W′ after a 90-degree (counterclockwise) rotation about the origin.(1 point)
W′(
,
)

Answer 11

To rotate a point \((x, y)\) by 90 degrees counterclockwise about the origin, we use the following rotation mapping rule:

\[ (x, y) \rightarrow (-y, x) \]

Now, let's apply this rule to point \(W(-3, 7)\):

1. Start with the coordinates of point \(W\):

   • \(x = -3\)
   • \(y = 7\)

2. Apply the 90-degree counterclockwise rotation:

   • The new x-coordinate: \(-y = -7\)
   • The new y-coordinate: \(x = -3\)

Thus, the coordinates of \(W'\) after the rotation are:

\[ W'(-7, -3) \]

Therefore, the answer is: W'(-7, -3).