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 Δ AOB where point O is the origin.

Answer 1

(a) Draw the graph of x + y = 6

                                               x + y = 6

x	6	3	0
y	0	3	6
(x, y)	(6, 0)	(3, 3)	(0, 6)

(b) In Δ AOB, by Pythagoras theorem,
AB² = OB² + O^A2 = 6² + 6² = 2 × 36 
∴ AB = 6`sqrt(2)`
OR, A(6, 0) and B(0, 6)
∴ d(A, B) `= sqrt((x_2-x_1)^2 + (y_2-y_1)^2) `

                `= sqrt((0-6)^2 + (6-0)^2) = sqrt((36+36) ) = sqrt(72) = 6sqrt(2)`
A(Δ AOB) `= 1/2` × product of sides making right angle
                 `= 1/2` × 6 × 6 = 18 sq. unit