Question

Draw a graph of the line $x+y=6$ which intersects the x and y axes at A and B respectively. Find the length of segment AB. Also, find the area of triangle OAB where O is the origin.

Answer 1

Hint: In this question, first we will find the coordinates of A and B. Now, triangle OAB will be a right angled triangle at O. So, we can find the area by the formula-
$\dfrac12\times\mathrm{Base}\times\mathrm{Height}$

Complete step-by-step answer:

From the graph it is clear that A(6, 0) and B(0, 6). Now, we have to find the length of AB using the distance formula-
$\mathrm{AB}=\sqrt{\left({\mathrm x}_2-{\mathrm x}_1\right)^2+\left({\mathrm y}_2-{\mathrm y}_1\right)^2}\\\mathrm{AB}=\sqrt{\left(6-0\right)^2+\left(0-6\right)^2}\\\mathrm{AB}=\sqrt{72}=6\sqrt2$
The area of triangle OAB is given by-
$=\dfrac12\times\mathrm{OA}\times\mathrm{OB}\\=\dfrac12\times6\times6\\=18\;\mathrm{square}\;\mathrm{units}$

This is the required answer.

Note: In such types of questions, it is better to take the help of the diagram to calculate the required distances and lengths. For example, here we can find the length of AB by applying Pythagoras’ Theorem in triangle AOB. Also, one should not forget to write the units in the final answer.