Question

select the notation that maps abc onto def. (a) (x,y)→(x - 5,y - 6) (b) (x,y)→(x - 6,y - 5)

Explanation:

Step1: Analyze translation in x - direction

To map one triangle onto the other, observe the horizontal shift. If we take a point on triangle ABC and its corresponding point on triangle DEF, say the x - coordinate of a vertex. The x - coordinate of a point on ABC is reduced by 6 to get the x - coordinate of the corresponding point on DEF. For example, if we consider a vertex of ABC at \(x = 0\), its corresponding vertex on DEF has \(x=- 6\). So the x - translation is \(x
ightarrow x - 6\).

Step2: Analyze translation in y - direction

Similarly, for the y - coordinate, the y - coordinate of a point on ABC is reduced by 5 to get the y - coordinate of the corresponding point on DEF. For example, if a vertex of ABC has \(y = 5\), its corresponding vertex on DEF has \(y = 0\). So the y - translation is \(y
ightarrow y - 5\).

Answer:

B. \((x,y)\to(x - 6,y - 5)\)