Question

Draw the graph of x + y=6 which intersects the X axis at A and B respectively. On the same graph paper, draw the graph of 2x-y=3 which intersects the X-axis and Y-axis at C and D respectively. E is the point of intersection of both the graphs. Find the areas of (a) ∆ECA (b) ∆EBD​

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Answer 1

Step-by-step explanation:

Given: Two lines x+y=6 and 2x-y=3

To find:Draw the graph of x + y=6 which intersects the X axis at A and B respectively. On the same graph paper, draw the graph of 2x-y=3 which intersects the X-axis and Y-axis at C and D respectively. E is the point of intersection of both the graphs. Find the areas of (a) ∆ECA (b) ∆EBD

Solution:

Step1: To draw x+y=6.

Put y=0 and find x,A(6,0)

and point B(0,6)

Step 2:To draw 2x-y=3.

Put y=0 and find x,C(1.5,0)

and point D(0,-3)

Step 3: Draw these lines,mark the intersection of both lines,point E(3,3).

Graph is attached.Fig 1

Step 4:See fig 2

Area of ∆ECA=1/2×BASE×HEIGHT

=1/2×AC×EF

=1/2×(4.5)×3

=6.75 unit²

Area of ∆ECA=6.75 unit²

Step 5:See fig 3

Area of ∆EBD=1/2×BASE×HEIGHT

=1/2×BD×EF

=1/2×(9)×3

=13.5 unit²

Area of ∆EBD=13.5 unit²

Final answer:

A(6,0)

B(0,6)

C(1.5,0)

D(0,-3)

E(3,3)

Area of ∆ECA=6.75 unit²

Area of ∆EBD=13.5 unit²

Hope it helps you.

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Answer 2

Step-by-step explanation:

Bio pe a

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