The image of an eraser in a magnifying glass is three times the eraser’s actual size and has a width of 14.4 cm. What is the actual width of the eraser in cm?
a) 14.4 cm.
b) 3 cm.
c) 43.2 cm.
d) 4.8 cm.
is it C?
A square has 16-cm sides. What is the perimeter of the image of this square after a dilation of 0.8?
a) 12.8 cm.
b) 51.2 cm.
c) 20 cm.
d) 80 cm.
is it A?
A dilation maps triangle LMN to triangle L’M’N’. MN = 14 in. and M’N’ = 9.8 in. If LN = 13 in., what is L’N’?
a) 18.6 in.
b) 9.1 in.
c) 9.8 in.
d) 0.7 in.
is it B?
since the image is 3 times the actual size, you want 14.4/3 = 4.8 for the actual size
The other two are correct.
Why did the eraser go to the magnifying glass? It wanted to see things up close and personal!
The actual width of the eraser would be 4.8 cm, so the correct answer is d) 4.8 cm.
Why did the square go to the gym? It wanted to work on its perimeter!
After a dilation of 0.8, the perimeter of the image of the square would be 12.8 cm, so the correct answer is a) 12.8 cm.
Why did the triangle go on a road trip? It wanted to explore different dimensions!
Since the dilation maps triangle LMN to triangle L’M’N’ and M’N’ is given as 9.8 in, L’N’ would be 9.1 in, so the correct answer is b) 9.1 in.
Yes, you are correct.
For the first question, the actual width of the eraser can be found by dividing the width of the image in the magnifying glass by the magnification factor. Since the image is three times the actual size and has a width of 14.4 cm, the actual width of the eraser would be 14.4 cm divided by 3, which is 4.8 cm. So the correct answer is (d) 4.8 cm.
For the second question, a dilation of 0.8 reduces the size of the square. To find the perimeter of the new image, we need to multiply the side length of the original square (16 cm) by the dilation factor (0.8). So the perimeter of the new image would be 16 cm multiplied by 0.8, which is 12.8 cm. Therefore, the correct answer is (a) 12.8 cm.
For the third question, we can use the fact that corresponding sides of similar triangles are proportional. If LN = 13 in. and M'N' = 9.8 in., then the ratio of LN to M'N' is 13/9.8. Since L'N' is corresponding to LN and is part of the same ratio, we can find it by multiplying the ratio by the length of L'N' (which is unknown).
So. (13/9.8) multiplied by L'N' equals 9.1 in. (since the ratio is equivalent to M'N'). Solving this equation gives us L'N' = (9.1 x 9.8) / 13. Therefore, the correct answer is (b) 9.1 in.
For the first question, we are given that the image of an eraser in a magnifying glass is three times the eraser's actual size and has a width of 14.4 cm. We want to find the actual width of the eraser.
To solve this, we can set up a proportion between the width of the image and the actual width of the eraser:
(image width)/(actual width) = (image size ratio)/(actual size ratio)
Let's represent the actual width of the eraser as "x." Then we have:
(14.4 cm)/(x cm) = (3)/(1)
Cross-multiplying, we get:
14.4 cm * 1 = x cm * 3
14.4 cm = 3x cm
Dividing both sides by 3, we find:
x cm = 4.8 cm
So, the actual width of the eraser is 4.8 cm.
Therefore, the correct answer is d) 4.8 cm.
For the second question, we have a square with 16-cm sides, and we need to find the perimeter of the image of this square after a dilation of 0.8.
To find the perimeter, we can multiply the length of one side of the image by 4, since a square has four equal sides.
The length of one side of the image after dilation can be found by multiplying the original length by the dilation factor (0.8). So, we have:
Length of one side of the image = (16 cm) * (0.8)
Length of one side of the image = 12.8 cm
Finally, we can find the perimeter of the image by multiplying the length of one side by 4:
Perimeter of the image = 12.8 cm * 4
Perimeter of the image = 51.2 cm
Therefore, the correct answer is b) 51.2 cm.
For the third question, we are given a dilation that maps triangle LMN to triangle L’M’N’. We know the lengths of MN and M’N’, and we need to find L’N’.
Based on the properties of a dilation, corresponding sides of the two triangles are proportional. Therefore, we can set up a proportion between LN and L’N’:
LN/L’N’ = MN/M’N’
Substituting the given values, we have:
13 in. / L’N’ = 14 in. / 9.8 in.
Cross-multiplying, we get:
13 in. * 9.8 in. = 14 in. * L’N’
127.4 in. = 14 in. * L’N’
Dividing both sides by 14, we find:
(L’N’) = 127.4 in. / 14 in.
(L’N’) = 9.1 in.
Therefore, the correct answer is b) 9.1 in.