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# Chapter 4: Exercises

Difficulty Level: At Grade Created by: CK-12

Note: A calculator may be necessary for some of these problems.

1. What is the distance between (13)\begin{align*}(1\text{, }3)\end{align*} and (88)\begin{align*}(8\text{, }8)\end{align*}?
2. What is the length of x\begin{align*}x\end{align*}?
3. Do the numbers 9, 18, and 24 make up a Pythagorean triple?
4. What is the area of the triangle below?
5. What is the circumference of the circle below?
6. What is the distance between (58)\begin{align*}(-5\text{, }-8)\end{align*} and (12)\begin{align*}(1\text{, }2)\end{align*}?
7. Is a triangle with side lengths of 8, 14, and 15 acute, obtuse, or right?
8. A baseball diamond includes four bases—first, second, third, and home—that are all 90 feet apart. The path a baserunner takes involves right angles at each of the bases. Imagine a player at bat with a runner on first. The pitcher throws a wild pitch and the player on first base goes for the steal to second. Once the catcher (at home base) gets a hold of the ball, he decides to throw it over the pitcher's head to second base. How far does the catcher have to throw the ball to get the player out?
9. Imagine that you get to put a TV in your room. However, there is only enough space for a television that is 17 inches long and 15 inches high. You've already purchased a 20-inch television. Will it fit inside the space you have prepared? (Recall that televisions are measured diagonally.)
10. Find the area of the triangle.
11. Erin hurt her leg at her soccer game but still has to walk home. To keep her leg from feeling worse, she wants to take the shortest possible route. Looking at the two possible routes below, determine how much shorter the red route is than the blue. Each block has a length of 100 meters.
12. Find two points on the line y=2\begin{align*}y=2\end{align*} that are 10 units from (24)\begin{align*}(2\text{, }-4)\end{align*}.
13. In the figure below, the angles at B\begin{align*}B\end{align*} and D\begin{align*}D\end{align*} are 90\begin{align*}90^\circ\end{align*}. Find the distance of AC+CE\begin{align*}AC+CE\end{align*}.
14. Instead of walking along two sides of a rectangular field, Ryan walked along the diagonal. By taking this shortcut, he saved a distance equal to half the length of the long side of the field. Find the length of the long side of the field given that the length of the shorter side is 78 meters.

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