Question

Draw a graph of X-Y+1=10 and 3X+2Y-12=0 and find the area of the triangle formed by these two lines and the X axis.Also shade the region.

Answer 1

x - y + 1 = 10 and 3x + 2y - 12 = 0

or x - y = 10 - 1 and 3x + 2y = 0 + 12

or x - y = 9 and 3x + 2y = 12

or x = 9 + y and 3x = 12 - 2y

or x = 9 + y and x = (12 - 2y)/3 = 4 - 2y/3

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In x = 9 + y,

if y = 1, x = 10

if y = 0, x = 9

if y = -1, x = 8

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In x = 4 - 2y/3,

if y = 0, x = 4

if y = 3, x = 2

if y = -3, x = 6

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Plotting these values on the graph paper (see attachment), we get a triangle  ABC, where the coordinates of A, B and C are (6, -3), (0-9) and (0,6) respectively.

On drawing a perpendicular AD from A on BC, we get D(0, -3).

On counting, we get BC = 15 units and AD = 6 units.

So, the area of the triangle is 1/2 * 6 * 15 = 3 * 15 = 45 square units.