Question

24 multiple choice 2 points two triangles are similar. the measure of the shortest side of the first triangle is 12 and the measure of the shortest side of the second triangle is 5. if the longest side of the first triangle measures 15, what is the measure of the longest side of the second triangle? 36 2.4 6.25 24 25 multiple choice 2 points what are the coordinates of a, the image of point a(-3,4), after a rotation of 180° about the origin? (-4,-3) (4,-3) (3,-4) (3,4)

Explanation:

Step1: Set up proportion for similar triangles

For similar triangles, the ratios of corresponding sides are equal. Let $x$ be the length of the longest side of the second triangle. The proportion is $\frac{12}{5}=\frac{15}{x}$.

Step2: Cross - multiply

Cross - multiplying gives $12x = 5\times15$.

Step3: Solve for $x$

$12x=75$, so $x=\frac{75}{12}=6.25$.

Step4: Recall rotation rule for 180 - degree rotation

When a point $(x,y)$ is rotated 180 degrees about the origin, the new coordinates $(x',y')$ are given by $x'=-x$ and $y'=-y$. For point $A(-3,4)$, after 180 - degree rotation, $x'=-(-3) = 3$ and $y'=-4$. So the coordinates of $A'$ are $(3,-4)$.

Answer:

1. C. 6.25
2. C. $(3,-4)$