Scale Factor as a Percent
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Basics on the topic Scale Factor as a Percent
After this lesson you will be able to make scale drawings and distortions using one or two scale factors as percents.
The lesson begins by relating the scale factor to the constant of proportionality, k. It leads to using a scale factor greater than one to enlarge the original drawing. It concludes with using two different scale factors to transform the original drawing into a distortion.
Learn how to use the scale factor as a percent by helping Leelee market her new brand!
This video includes key concepts, notation, and vocabulary such as: constant of proportionality, k (the scale factor between two similar objects); reduction (a scaled-down picture of the original image where k<1); enlargement (a scaled-up picture of the original image where k>1); scale drawing (a reduction or enlargement of an original image); and distortion (a complete transformation of an object so that it does not look like the original).
Before watching this video, you should already be familiar with scale factors, the constant of proportionality, and determining whether a scale drawing is a reduction or an enlargement.
After watching this video, you will be prepared to find the scale factor given two scale drawings.
Common Core Standard(s) in focus: 7.RP.A.2b, 7.G.A.1 A video intended for math students in the 7th grade Recommended for students who are 12-13 years old
Transcript Scale Factor as a Percent
Leelee knows she's got what it takes to become internet famous. So she decides to follow in the footsteps of her favorite celebs and create her own brand. LeeLee Lifestyle: Just Be. To get the word out about her new brand, Leelee plans to make a diverse line of eye-catching posters. But in order to use her digital design software, she's going to also need to use the scale factor as a percent Leelee originally designed her logo to fit on a poster measuring five feet wide and eight feet high. But the launch of an exciting new brand deserves something larger! If she wants to make the dimensions of the poster three hundred percent larger, what will the new dimensions be? You may remember that the scale factor is the same as the constant of proportionality, 'k', between two similar objects. Any length on a scale drawing is equal to the scale factor times the corresponding length on the original drawing. With this formula, we can find the scaled dimensions of Leelee's poster, just by substituting in our known values. Looking at the information we have been provided, what should we use for our scale factor? Leelee wants to increase the dimensions by three hundred percent so we can use 3 as our value for 'k'. Now, how can we use this formula to find our scaled width? We know the original width is five feet, so multiplying that by our scale factor give us the scaled width of fifteen feet. Now, to for the height. The original height of eight feet times our scale factor, 'k' gives us the scaled dimension of twenty four feet. As we expected, our scale factor is greater than one, so the result is an enlargement of the original. "Leelee’s extra-large launch poster is ready to go!" For her next poster, Leelee needs to take her original design, which is tall and skinny, and transform it into something completely different. To do this, she is going to use two DIFFERENT scale factors. For the vertical height, she will use a scale factor of 75 percent. For the horizontal width, she will use a scale factor of 250 percent. A change like this which uses multiple scale factors is called a distortion, because the resulting shape may not look anything like the original. Before we start figuring out the new dimensions, how do you imagine her new poster will look? Well, for the height we have a scale factor less than one, so that is going to create a VERTICAL SHRINK. This means the resulting shape will be shorter than the original. For the width, we have a scale factor of more than one, so that is going to create a HORIZONTAL STRETCH. This means the resulting shape will be wider than the original. Ok, now that we know what kind of distortion we should expect, let's calculate our new dimensions using our formula. We know that our original height is 8 feet and we want to apply a scale factor of 75 percent, or 0.75. That gives us a scaled height of 6 feet. Now that we've done our vertical shrink, let's move on to the horizontal stretch. Once again, plugging in our constant of proportionality and the original width into our formula gives us a scaled width of 12.5 feet. Leelee's new distorted poster would look great on the side of a bus! Or maybe even a really, really big hot dog bun! For her last guerilla marketing effort, Leelee wants to make another distortion. This time, she wants to use a whopping nine hundred and sixty percent for her vertical scale factor. And one fifth for the horizontal scale factor,. Before we figure out the new dimensions, how do you imagine THIS distorted poster will look? Since we are using a scale factor greater than one applied only to the height, that will create a VERTICAL STRETCH. Our other scale factor is less than one and is applied only to the width, that will create a HORIZONTAL SHRINK. Now that we know roughly what kind of shape we can expect, let's calculate our new dimensions. Our vertical stretch uses a scale factor of 960 percent, or 9.6. We multiply that by our original height of 8 feet giving us a scaled height of 76.8 feet. Our horizontal shrink uses a scale factor of one fifth, so that goes in for 'k'. Multiplying that by our original width of 5 feet gives us a new width of one foot. "While Leelee’s posters are being printed, let’s review." The scale factor, 'k', is the constant of proportionality describing the relationship between two related drawings. It can be written as a fraction, decimal, or a percent. If you apply different scale factors to different dimensions, you create a distortion of the original. Distortions applied to the width result in a horizontal stretch...or shink. Distortions applied to the height result in vertical stretch...or shrink. "Leelee's prints are back and she's all set to unveil her brand new marketing campaign!" "Whoa...guess we went a little overboard on the distortion!" Hashtag epic fail!