A shopkeeper rearranges a price-tag icon, triangle \(O\) with vertices \((0, -3)\), \((0, 0)\), \((3, -3)\), on the shelf-edge label strip by sliding it alo...
Question 1 Report
A shopkeeper rearranges a price-tag icon, triangle \(O\) with vertices \((0, -3)\), \((0, 0)\), \((3, -3)\), on the shelf-edge label strip by sliding it along the strip using the vector \(\binom{-5}{3}\), so the discounted item lines up under its new price band.
- Write down the coordinates of the image of triangle \(O\). (3)
- Write down the column vector used for this translation. (1)
Answer Details
This question tests translating a shape given directly by coordinates and reading off the image and the vector used.
Triangle \(O\) has vertices \((0,-3)\), \((0,0)\) and \((3,-3)\). A translation by the vector \(\binom{-5}{3}\) subtracts \(5\) from every \(x\)-coordinate and adds \(3\) to every \(y\)-coordinate:
\[(0,-3)\to(-5,0),\qquad(0,0)\to(-5,3),\qquad(3,-3)\to(-2,0)\](a) The image has vertices \((-5,0)\), \((-5,3)\) and \((-2,0)\), shown below sliding along the shelf-edge strip. [3] (1 mark per correct vertex)
(b) The column vector used for this translation is \(\binom{-5}{3}\). [1]
Sliding a shape "along a strip" is exactly what a translation does: it moves every point the same fixed distance in the same fixed direction, with no rotation or resizing, which is why the negative \(x\)-component and positive \(y\)-component are applied identically to every vertex.
Download The App On Google Playstore
Everything you need to excel in your exams
