Question

1. draw the image of the triangle under the transformation (x,y)→(x + 3,y + 4).
2. use the transformation (x,y)→(x + 7,y + 3) to translate (0, - 4). what are the coordinates of the image?
3. use the transformation (x,y)→(x + 1,y - 3) to translate (5,7). what are the coordinates of the image?
4. use the transformation (x,y)→(x - 7,y + 8) to translate (0, - 9). what are the coordinates of the image?

Explanation:

Step1: Apply transformation rule for question 2

For the transformation $(x,y)\to(x + 7,y+3)$ and the point $(0,-4)$, substitute $x = 0$ and $y=-4$ into the rule.
New $x$ - coordinate: $x'=0 + 7=7$
New $y$ - coordinate: $y'=-4 + 3=-1$

Step2: Apply transformation rule for question 3

For the transformation $(x,y)\to(x + 1,y - 3)$ and the point $(5,7)$, substitute $x = 5$ and $y = 7$ into the rule.
New $x$ - coordinate: $x'=5+1 = 6$
New $y$ - coordinate: $y'=7-3 = 4$

Step3: Apply transformation rule for question 4

For the transformation $(x,y)\to(x - 7,y + 8)$ and the point $(0,-9)$, substitute $x = 0$ and $y=-9$ into the rule.
New $x$ - coordinate: $x'=0-7=-7$
New $y$ - coordinate: $y'=-9 + 8=-1$

Answer:

1. $(7,-1)$
2. $(6,4)$
3. $(-7,-1)$

(Note: For question 1, a visual drawing is required. The general approach is to take each vertex of the triangle, apply the transformation $(x,y)\to(x + 3,y + 4)$ to find the new - coordinates of the vertices, and then draw the new triangle with the transformed vertices on the same coordinate - grid.)