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Scale Factor & Scale Drawings. Understanding Scales. All scale drawings must have a scale written on them. Scales are usually expressed as ratios. Normally for maps and buildings the ratio: Drawing length: Actual length For maps the ratio is normally in the ratio:

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## Scale Factor & Scale Drawings

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**Scale Factor &**Scale Drawings**Understanding Scales**All scale drawings must have a scale written on them. Scales are usually expressed as ratios. Normally for maps and buildings the ratio: Drawing length: Actual length For maps the ratio is normally in the ratio: Map distance: Actual Distance Example: 1cm : 100cm The ratio 1cm:100cm means that for every 1cm on the scale drawing the length will be 100cm in real life Example: 1:10000 The ratio 1:10000 means that the real distance is 10000 times the length of one unit on the map or drawing.**How to find Scale Factor**• When a figure is dilated, its size is changed by multiplying the length of each side by a scalefactor. All angles remain the same and so the new shape (or image) is similar to the original. • Can be found by dividing a new side length by the original side length. • When going from a small shape to a larger shape the scale factor is greater than 1. (Enlargement) • When going from a large shape to a smaller shape the scale factor is • less than 1. (Reduction) • Determine the corresponding side lengths. • Determine if you are making a larger shape or a smaller shape. • Determine if the scale factor is greater than or less than 1. • Write the correct ratio.**new**SF old Scale Factor Scale factor = new measurement old measurement Old measurement x SF = new measurement • Scale factor more than 1 => shape gets bigger • (Enlargement) • Scale factor less than 1 => shape gets smaller • (Reduction) • Congruent shapes are similar shapes with SF = 1**Vocabulary**scale model scale factor scale scale drawing**The scale can be written as a scale factor, which is the**ratio of the length or size of the drawing or model to the length of the corresponding side or part on the actual object. • Scale Factor needs to be the SAME UNITS!**This HO gauge model train is a scale model of a historic**train. A scale model is a proportional model of a three-dimensional object. Its dimensions are related to the dimensions of the actual object by a ratio called the scale factor. The scale factor of an HO gauge model train is . 1 87 1 87 This means that each dimension of the model is of the corresponding dimension of the actual train.**A scale is the ratio between two sets of measurements.**Scales can use the same units or different units. The photograph shows a scale drawing of the model train. A scale drawingis a proportional drawing of an object. Both scale drawings and scale models can be smaller or larger than the objects they represent.**If you have ever seen Jurassic**Park, you saw how big the dinosaurs were compared to the people. Pretend that they made a large Human to watch over the animals. What would be the scale factor if a 64 inch person was made to be 160 feet?**The scale factor tells you**how many times bigger than “normal” that person really is. You must make all units of measure the same…. 64 inches 64 inches 64 inches = = 160 feet 1920 inches 160 x 12**Now take the:**64 inches And simplify 1920 inches 1/30 inches This means that the person was created 30 times his normal size.**The scale factor of the pool is**1” to 20 yards. Or = Scale Factor**Keep like**units in the same fraction. Inches = yards Inches yards Setting up Proportions**Remember…**• There is more than one way to set up a proportion correctly! • Cross Multiply! • Use common sense!**Tom is drawing a blueprint for a rectangular shed he wants**to build. The scale factor is 1 ft. to ¼ inch. If the dimensions of the blueprint are 1 ¼ in. by 2 inches, what are the actual dimensions of the shed going to be? Write a Proportion Using Scale Factor**¾ inch to 1 foot**If the length in inches is 2 ¼ inch, what would the actual length be in feet ? Write a ProportionUsing a Scale Factor**What are scale drawings?**Scale drawings are everywhere! Scale Drawings On Maps Vehicle design Footprints of houses Can you think of any more?**6cm**Scale 1 cm = 1 m Length of units = 6 m Scale in everyday life: kitchen design 5**Scale in everyday life: maps**Scale 1 : 1 000 000**Scale in everyday life: plans**decking path pool Scale 2 cm = 1 m 7**When objects are too small or too large to be drawn or**constructed at actualsize, people use a scale drawing or a model.The scale drawing of this tree is 1:500If the height of the tree on paper is 20 inches, what is the height of the tree in real life?**The scale is the relationship between the measurements of**the drawing or model to the measurements of the object. In real-life, the length of this van may measure 240 inches. However, the length of a copy or print paper that you could use to draw this van is a little bit less than 12 inches**Map Scales**• Map Scales (Legends) are used to find distances on a map. • For example, if your map legend tells you that ½ of an inch represents 50 miles, how could you find the mileage for a 2 inch distance on the map?**Map Scales**Ratios and proportions can be used to find distances using a scale. Example: 1 inch = 15 miles The distance from Jacksonville to Smithtown on a map is 4 inches. How many miles are between these cities? 1 in. 15 mi. 4 in n = The distance between the two cities is 60 miles. 1n = 60 n = 60

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