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High School Math : Graphing

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Example Question #1 : Graphing

The vertices of a triangle are given by $(0,3), \; (0,5),\; and \; (-2,4)$ $\displaystyle (0,3), \; (0,5),\; and \; (-2,4)$. The triangle is rotated about the origin by $\displaystyle 90$ degrees clockwise. What are the new coordinates?

Possible Answers:

$(6,0), \; (10,0),\; and \; (8,4)$ $\displaystyle (6,0), \; (10,0),\; and \; (8,4)$

$(-9,0), \; (-15,0),\; and \; (-12,-6)$ $\displaystyle (-9,0), \; (-15,0),\; and \; (-12,-6)$

$(4,1), \; (6,1),\; and \; (5,3)$ $\displaystyle (4,1), \; (6,1),\; and \; (5,3)$

$(3,0), \; (5,0),\; and \; (4,2)$ $\displaystyle (3,0), \; (5,0),\; and \; (4,2)$

$(-3,0), \; (-5,0),\; and \; (-4,-2)$ $\displaystyle (-3,0), \; (-5,0),\; and \; (-4,-2)$

Correct answer:

$(3,0), \; (5,0),\; and \; (4,2)$ $\displaystyle (3,0), \; (5,0),\; and \; (4,2)$

Explanation:

The coordinates form a triangle in the second quadrant with a side along the y-axis. The rotation about the origin by $\displaystyle 90$ degrees clockwise results in a triangle in the first quadrant with a side along the x-axis. There are two responses that give triangles along the x-axis:

$(3,0), \; (5,0),\; and \; (4,2)$ $\displaystyle (3,0), \; (5,0),\; and \; (4,2)$ and

$(6,0), \; (10,0),\; and \; (8,4)$ $\displaystyle (6,0), \; (10,0),\; and \; (8,4)$

A rotation and a dialation by a factor of $\displaystyle 2$ is given by

$(6,0), \; (10,0),\; and \; (8,4)$ $\displaystyle (6,0), \; (10,0),\; and \; (8,4)$, so the correct answer is $(3,0), \; (5,0),\; and \; (4,2)$ $\displaystyle (3,0), \; (5,0),\; and \; (4,2)$

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High School Math : Graphing

Study concepts, example questions & explanations for High School Math

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Example Question #1 : Graphing

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