Question

Draw the graph of $x+y=6$ which intersects the X-axis and the Y-axis at A and B respectively. Find the length of seg AB. Also, find the area of $\Delta$AOB where point O is the origin.

Answer 1

Given equation $x+y=6$

divide $6$ on both sides

$\frac{x}{6}+\frac{y}{6}=\frac{6}{6}$

$\frac{x}{6}+\frac{y}{6}=1$

on comparing $\frac{x}{a}+\frac{y}{b}=1$

Menas at x-axis intercept point $a$ and y-axis intercept point $b$

$A(6,0),B(0,6)$

$x_1{y}_1$ $x_2{y}_2$

By using distance formula

$AB=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$

$AB=\sqrt{{(0-6)}^2+{(6-0)}^2}=\sqrt{36+36}$

$AB=\sqrt{2.36}$

$AB=6\sqrt{6}$

Area of $△AOB=\frac{1}{2}\times base\times height$

$=\frac{1}{2}\times 6\times 6$

$=18{cm}^2$