Question

1. if a character in a video game is scaled up by a factor of 3, what happens to the corresponding sides of the triangles in the model? a. they triple in length b. they stay the same c. they halve in length d. they double in length 8. when using aa similarity in coordinate geometry, which of the following tools is commonly used? a. area formula b. slope formula c. compass d. protractor 9. if ∠p = ∠s, pq = 18 m, pr = 24 m, and st = 12 m, find the missing side su to prove similarity between △pqr and △stu using sas. a. 18 m b. 16 m c. 14 m d. 20 m

Explanation:

Step1: Understand scaling concept

Scaling a model by a factor of 3 means multiplying each side - length by 3. So the sides of the triangles in the model triple in length.

Step2: Recall AA - similarity tools

In coordinate geometry, to use AA (angle - angle) similarity, we need to find the measure of angles. The slope formula is used to find the slope of lines which helps in finding the angles between lines.

Step3: Apply SAS (side - angle - side) similarity

If \(\angle P=\angle S\), for \(\triangle PQR\) and \(\triangle STU\) to be similar by SAS, we have the proportion \(\frac{PQ}{ST}=\frac{PR}{SU}\). Given \(PQ = 18m\), \(PR = 24m\), and \(ST = 12m\). Substitute into the proportion: \(\frac{18}{12}=\frac{24}{SU}\), cross - multiply gives \(18\times SU=12\times24\), then \(SU=\frac{12\times24}{18}=16m\).

Answer:

1. a. They triple in length
2. b. Slope formula
3. b. 16m