By translating triangle ABC 4 units up and 3 units left to form triangle A'B'C' means that the line joining each of the corresponding points represents the hypothenus of a right triangle with legs 4 units and 3 unit. To find the length of each corresponding points, we use the prthagoras theorem which states that the square of the length of the pythagoras of a right triangle is equal to the sum of the squares of the lenght of other legs. i.e. the square of the required distance = 4^2 + 3^2 = 16 + 9 = 25 Therefore, the distance of eachcorresponding side is given by the square root of 25 = 5.