Coordinate Geometry - Area of Rectilinear Figures

A landscape designer uses a coordinate plan to mark out a triangular garden. Each coordinate unit represents 1 metre.
Two corners are \(B(0.5,1)\) and \(C(3.5,1)\). The third corner, \(A\), lies at the intersection of the lines
\[y=2x+1 \quad\text{and}\quad y=5.6.\] Answer the following on graph paper. Use a scale of \(2\) cm to represent \(1\) unit on each axis, with \(0\leq x\leq4\) and \(0\leq y\leq10\).

1. Draw the graph of \(y=2x+1\) for \(0\leq x\leq4\).

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2. Draw the line \(y=5.6\). Label its intersection with your graph \(A\), and state the coordinates of \(A\).

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3. Plot \(B\) and \(C\), and join \(AB\), \(AC\) and \(BC\) to show the garden.

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4. Find the area of the garden.

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5. Corner \(A\) is moved horizontally to \(A'(3,5.6)\), while \(B\) and \(C\) remain fixed. Does the area change? Explain your answer without calculating the area again.

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