Question

given △abc with ab contained in the line 2x + 3y = 5. if △abc is dilated to get △abc, which of the following lines could contain ab? 2x + 3y = 10, 3x + 2y = 10, 3x - 2y = 10, 2x - 3y = 10

Explanation:

Step1: Recall dilation property

Dilation of a figure results in parallel lines for corresponding sides. The line containing a side of the dilated triangle will be parallel to the line containing the corresponding side of the original triangle.
For two lines \(Ax + By=C_1\) and \(Ax + By = C_2\), they are parallel.
The line containing \(AB\) is \(2x + 3y=5\).

Step2: Identify parallel line

We need to find a line of the form \(2x + 3y = k\) (where \(k
eq5\)) among the options.
The line \(2x + 3y = 10\) has the same coefficients of \(x\) and \(y\) as \(2x+3y = 5\), so it is parallel to the line containing \(AB\).

Answer:

\(2x + 3y=10\)