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 ∆ AOB where point O is the origin.

Answer 1

Answer:

$AB=6\sqrt2units.$

Area of triangle AOB is 18 squnits.

Step-by-step explanation:

Given the equation of graph. we have to draw the graph and to find the length of AB with the area of ΔAOB.

Points A and B are (6,0) and (0,6).

Using distance formula,

$AB=\sqrt{(0-6)^2+(6-0)^2}\sqrt{72}=6\sqrt2units.$

Now, area of ΔAOB

$=\frac{1}{2}\times base\times height\\\\=\frac{1}{2}\times6\times6\\\\=18\thinspace units^2$

hence, area of triangle AOB is 18 squnits.

Answer 2

Step-by-step explanation:

Given equation x+y=6

on comparing ax + by =1

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

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

(x1, y1) (x2, y2)

By using distance formula

AB= ( x2−x1 )^2 +( y 2−y 1 )^2

AB= (0−6)^2 + (6−0)^2

AB = 36+36

AB=6

Area of △AOB= 1/2 ×base×height

= 1/2×6×6

=18cm^2