The Internet

Log In or Register

 of Δ DEF ?

The scale factor of Δ DEF is 2.

Ask AI on The Internet

Question: In the xy-coordinate plane, Δ ABC has vertices at A(1, -2), B(1, 0.5), and C(2, 1) and Δ DEF has vertices at D(4, -3), E(4, 2), and F(6, 3). The triangles are similar because Δ DEF is the image of Δ ABC under a dilation. what is the scale factor

Asked by TaureanHilton

0 Points

Log In or Register to Vote

To find the scale factor of the dilation, we first need to find the lengths of corresponding sides in both triangles. Let's find the length of side AB in ΔABC and side DE in ΔDEF. Side AB in ΔABC has the coordinates A(1, -2) and B(1, 0.5). Using the distance formula: AB = √((1 - 1)^2 + (0.5 - (-2))^2) = √((0)^2 + (2.5)^2) = √(6.25) = 2.5 Side DE in ΔDEF has the coordinates D(4, -3) and E(4, 2). Using the distance formula: DE = √((4 - 4)^2 + (2 - (-3))^2) = √((0)^2 + (5)^2) = √(25) = 5 Now let's find the scale factor (k) using the ratio of corresponding side lengths: k = (side length of ΔDEF) / (side length of ΔABC) k = DE / AB = (5) / (2.5) = 2 Therefore, the scale factor of the dilation is 2.

Answered by gpt-4

June 21, 2023, 10:42 a.m.

0 Points

Log In or Register to Vote

Think your answer is better than the AI's? Post it below.

Please log in or sign up to post your answer.

This article was generated in part by one of OpenAI’s large-scale language-generation model, answering user TaureanHilton's question. Images were generated with OpenAI's AI model, DALL·E 2. The Internet takes ultimate responsibility for the content of this publication.
If you want your question answered by an AI, click here.

Published: Wednesday, June 21, 2023

Comment Section