Let’s write equations for lines.
The following diagram shows how to find an equation for a line and use that to decide which points are on that line.
A dilation with scale factor 2 sends A to B. Where is the center of the dilation?
Here is a line.
There are many different ways to write down an equation for a line like the one in the problem. Does (y - 3)/(x - 6) = 2 represent the line? What about (y - 6)/(x - 4) = 5? What about (y + 5)/(x - 1) = 2? Explain your reasoning.
We get select any point on the line for example (7,7)
(7 - 3)/(7 - 6) = 4/1 ≠ 2
(7 - 6)/(7 - 4) = 1/3 ≠ 5
(7 + 5)/(7 - 1) = 12/6 = 2
Here is triangle ABC.
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