A triangle with vertices A(1, 1), B(2, 3) and C(4, 1) is mapped onto its image by a translation T = [-4, 1]. Find the coordinates of the images of triangle ABC.

Here are the solutions for ITEM 3 and ITEM 4. ITEM 3 Some S.2 students of Taibah international school obtained the following marks in a Math test. | Name | Grade | |-------------|-------| | Daniel | 80 | | Tendo | 78 | | Christopher | 84 | | Hannah | 80 | | Nicole | 92 | | Joshua | 84 | a) Illustrate the mapping of marks to students. To illustrate the mapping, we show the relationship from the set of students to the set of grades. Students Grades • Daniel 80 • Tendo 78 • Christopher 84 • Hannah 80 • Nicole 92 • Joshua 84 b) What type of mapping is this? This is a many-to-one mapping. This is because multiple students (e.g., Daniel and Hannah) map to the same grade (80), and multiple students (e.g., Christopher and Joshua) map to the same grade (84). ITEM 4 a) A triangle with vertices A(1, 1), B(2, 3) and C(4, 1) is mapped onto its image by a translation T = -4 \\ 1 . Find the coordinates of the images of triangle ABC. To find the image of a point (x, y) under a translation T = h \\ k , the new coordinates (x', y') are given by (x+h, y+k). Step 1: Find the image of vertex A. For A(1, 1) and T = -4 \\ 1 : A' = (1 + (-4), 1 + 1) = (1 - 4, 2) = (-3, 2) Step 2: Find the image of vertex B. For B(2, 3) and T = -4 \\ 1 : B' = (2 + (-4), 3 + 1) = (2 - 4, 4) = (-2, 4) Step 3: Find the image of vertex C. For C(4, 1) and T = -4 \\ 1 : C' = (4 + (-4), 1 + 1) = (4 - 4, 2) = (0, 2) b) Evaluate the following. If a = 4 \\ 2 and b = 2 \\ -3 , find: (i) 2a Step 1: Multiply the vector a by the scalar 2. 2a = 2 4 \\ 2 = 2 × 4 \\ 2 × 2 = 8 \\ 4 (ii) 2a + 3b Step 1: Calculate 2a. From part (i), we know: 2a = 8 \\ 4 Step 2: Calculate 3b. 3b = 3 2 \\ -3 = 3 × 2 \\ 3 × (-3) = 6 \\ -9 Step 3: Add the resulting vectors 2a and 3b. 2a + 3b = 8 \\ 4 + 6 \\ -9 = 8 + 6 \\ 4 + (-9) = 14 \\ 4 - 9 = 14 \\ -5 3 done, 2 left today. You're making progress.