Geometry Unit Exam Part 1

A decagon is a polygon with ten sides. This means that it has ten straight line segments that connect to form a closed shape. Each side of a decagon is equal in length and the sum of all its interior angles is equal to 1440 degrees. Therefore, the correct answer is 10 sides.

A stop sign is shaped like an octagon because it has eight sides. The octagon shape is easily recognizable and distinguishes a stop sign from other types of signs. The eight sides provide enough space for the word "STOP" to be clearly displayed in white letters. Additionally, the octagonal shape helps to draw attention and alert drivers to come to a complete stop at intersections.

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If Ms. Schaaf drives west for 4 miles and then north for 1 mile, she would be traveling along the two sides of a right triangle. The distance she would have to drive directly to Kezar Stadium would be the length of the hypotenuse of this triangle. Using the Pythagorean theorem, we can calculate the length of the hypotenuse as the square root of the sum of the squares of the two sides. In this case, the length of the hypotenuse would be approximately 4.1 miles.

The given answer, equilateral, suggests that the triangle shown below is an equilateral triangle. An equilateral triangle is a type of triangle in which all three sides are of equal length. This means that all angles in an equilateral triangle are also equal, measuring 60 degrees each.

A polygon with five sides is called a pentagon.

Ms. Schaaf stands 9 feet away from the bottom of the flag pole because the distance between her and the top of the flag pole is 15 feet, and the flag pole is 12 feet tall. To find the distance from the bottom of the flag pole, we subtract the height of the flag pole from the total distance, which gives us 15 - 12 = 3 feet. Since Ms. Schaaf is standing above the bottom of the flag pole, we subtract this distance from the total distance, which gives us 3 - 12 = 9 feet.

Based on the given information, the triangle shown below is a right triangle. A right triangle is a triangle that has one angle equal to 90 degrees.

The slope-intercept form of a line is represented by the equation y = mx + b, where m is the slope of the line and b is the y-intercept. This equation allows us to easily identify the slope and y-intercept of a line by looking at the coefficients of the variables. Therefore, the correct answer is y = mx + b.

The equation of the line that goes through the given points is not y = -3x + 2.

The point (1,1) is not on the line y = 2x + 1 because when we substitute x = 1 into the equation, we get y = 2(1) + 1 = 3, which is not equal to 1. Therefore, the point (1,1) does not satisfy the equation and is not on the line.

The ladder forms a right triangle with the wall and the ground. The length of the ladder is the hypotenuse of the triangle, and the distance from the bottom of the ladder to the bottom of the building is one of the legs. Using the Pythagorean theorem (a^2 + b^2 = c^2), we can calculate the length of the other leg, which represents the height up the wall that the ladder reaches. In this case, the calculation would be 5^2 + b^2 = 15^2. Solving for b, we find that b is approximately 14.1 feet.

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The rotation that occurred above can be described as a rotation of 90 degrees counter clockwise. This means that the object or shape was rotated in the opposite direction of the clock's movement by an angle of 90 degrees.

The transformation shown above is a dilation of 2 because all the points on the figure have been expanded or contracted by a scale factor of 2 from the original figure. This means that each point on the figure has been moved twice as far away from or closer to the center of dilation compared to its original position.

The two lines have the same slope (-2) but different y-intercepts (5 and -3). This means that the lines are parallel and will never intersect.

The given transformation involves shifting the coordinates of a point by a certain amount. The x-coordinate is shifted 7 units to the right and the y-coordinate is shifted 3 units downwards. This can be observed in all the given options, but the correct answer is (x-7, y-3) because it accurately reflects the direction and magnitude of the shift.

The slope of a line is a measure of how steep it is. In this case, the slope of the line is -1/2. This means that for every 1 unit increase in the horizontal direction, the line decreases by 1/2 unit in the vertical direction. It has a negative sign because the line is sloping downwards from left to right.

A translation that moves 6 units down and 5 units to the right can be described as ( x + 5 , y - 6 ). This is because when we move down, the y-coordinate decreases, so we have y - 6. Similarly, when we move to the right, the x-coordinate increases, so we have x + 5.

The given answer states that the transformation shown is a reflection over the line y = -2. This means that every point on the original figure is reflected across the line y = -2 to create the transformed figure. The line y = -2 acts as the mirror line, with all points on one side of the line being flipped to the other side while maintaining the same distance from the line.