#### 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.

#### Solution

(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,

AB^{2} = OB^{2} + O^{A2} = 6^{2} + 6^{2} = 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

Is there an error in this question or solution?

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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. Concept: Graphical Method of Solution of a Pair of Linear Equations.

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