Chapter 3.2, Problem 70SR

To determine

To find:The coordinate of the vertices of the image of given triangle $ABC$ in coordinate plane after the translation 4 units up and 1 unit right and also plot graphs of both the triangles.

Answer to Problem 70SR

The coordinates of the vertices of the image of triangle $ABC$ i.e. of triangle $A`B`C`$ are$A`\left(2,5\right),B`\left(5,6\right),C`\left(1,8\right)$ .

It’s image is shown as follows:

  

Explanation of Solution

Given information: 

The triangle $ABC$ is shown in XY plane, with its vertices as $A\left(1,1\right),B\left(4,2\right),C(0,4)$ .

Concept used: 

When a point is shifted few units in right side, these units are added in its x coordinate and when it is shifted few units in up direction, these units are also added in given y coordinates. So, to get the coordinates of imaged triangle, add 1 in each corresponding x coordinate and add 4 in each corresponding original y coordinate.

Calculation:

Based on above concept or formula used, the coordinates of vertices of imaged triangle $A`B`C`$ will be,

  $\begin{array}{l} A`=\left(1+1,1+4\right)=\left(2,5\right)\\ B`=\left(4+1,2+4\right)=\left(5,6\right)\\ C`=\left(0+1,4+4\right)=\left(1,8\right)\end{array}$

Conclusion:The required coordinates of image of triangle ABC be $A`\left(2,5\right),B`\left(5,6\right),C`\left(1,8\right)$ and its required image is given as: