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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. - Algebra

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,
AB2 = OB2 + OA2 = 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

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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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