Given a triangle with vertices at A(1,3), B(4,7) and C(6,2) it undergoes two successive translation first by vector V1 = (2/3) and second by vector V2 = (-4/-1). Find the final coordinate of the triangle and explain how the composition of these translation affect the overall position movement.

Step 1: Find the resultant translation vector. To find the overall translation, we add the two translation vectors V_1 and V_2. V_total = V_1 + V_2 = 2 \\ 3 + -4 \\ 6 V_total = 2 + (-4) \\ 3 + 6 = -2 \\ 9 Step 2: Apply the resultant translation vector to each vertex of the triangle. For a point (x, y) and a translation vector a \\ b , the new point is (x+a, y+b). For vertex A(1, 3): A' = (1 + (-2), 3 + 9) = (1 - 2, 3 + 9) = (-1, 12) For vertex B(4, 7): B' = (4 + (-2), 7 + 9) = (4 - 2, 7 + 9) = (2, 16) For vertex C(6, 2): C' = (6 + (-2), 2 + 9) = (6 - 2, 2 + 9) = (4, 11) The final coordinates of the triangle are A'(-1, 12), B'(2, 16), C'(4, 11). Step 3: Explain how the composition of these translations affects the overall movement. The composition of two successive translations is equivalent to a single translation by the sum of the individual translation vectors. In this case, the triangle undergoes an overall translation by the vector -2 \\ 9 . This means the entire triangle moves 2 units to the left and 9 units upwards from its original position. Send me the next one 📸