Straight-Line Graphs Structured Questions | Cambridge IGCSE Additional Mathematics

Question 1 of 4 · 10 marks

Straight-Line Graphs · 2 - Perpendicular Lines & Coordinate Geometry of Rectangles

4 parts

Additional Mathematics 0606 · Question 1Paper 2 · Calculator[10 marks]

The line $L_1$ has equation $2x + 3y - 12 = 0$ and intersects the $y$ -axis at point $A$ .

(a)

State the coordinates of point $A$ .

[1]

(b)

The line $L_2$ passes through $A$ and is perpendicular to $L_1$ . Find the equation of line $L_2$ in the form $y = mx + c$ .

[3]

(c)

Line $L_2$ intersects the $x$ -axis at point $B$ . Find the coordinates of $B$ .

[2]

(d)

Point $D$ is such that $OADB$ forms a rectangle, where $O$ is the origin. Determine the coordinates of $D$ and calculate the exact length of diagonal $AB$ , leaving your answer in simplified surd form.

[4]