Parallel and perpendicular linesIB MYP Maths Standard: Subtopic test

1. 1
   A line $L$ has equation $y=3x-2$.

   (a)

   What is the gradient of any line parallel to $L$?

   [1 mark]

   • A$-3$
   • B$3$
   • C$-2$
   • D$-\frac13$

   (b)

   What is the gradient of any line perpendicular to $L$?

   [1 mark]

   • A$-\frac13$
   • B$3$
   • C$\frac13$
   • D$-3$

   (c)

   Find the equation of the line parallel to $L$ that passes through the point $(2,1)$.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A line $M$ has equation $2x+4y=8$.

   (a)

   What is the gradient of $M$?

   [1 mark]

   • A$2$
   • B$-2$
   • C$\frac12$
   • D$-\frac12$

   (b)

   What is the gradient of a line perpendicular to $M$?

   [1 mark]

   • A$-2$
   • B$\frac12$
   • C$2$
   • D$-\frac12$

   (c)

   Determine whether the line $y=2x+7$ is perpendicular to $M$. Justify your answer.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A line $p$ has equation $y=\frac12x+1$, and $P$ is the point $(4,5)$.

   (a)

   Find the equation of the line through $P$ that is perpendicular to $p$.

   [3 marks]

   (b)

   The perpendicular through $P$ meets $p$ at the point $Q$. Find the coordinates of $Q$, and hence the shortest distance from $P$ to $p$, to 3 significant figures.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A town planner in Lisbon is designing roads on a coordinate grid where 1 unit represents 100 m. The main road is a straight line through $A(0,2)$ and $B(6,5)$.

   (a)

   (i) Find the equation of the main road.
   (ii) A new road passes through $C(2,0)$ and must never meet the main road. Find the equation of the new road and justify why the two roads never meet.

   [6 marks]

   (b)

   A straight footpath is to be built from a bus stop at $D(1,8)$ to the main road, so that it is as short as possible. Find the equation of the footpath, the coordinates of the point where it meets the main road, and the length of the footpath in metres, to 3 significant figures.

   [6 marks]

   Total for question 4: 12 marks

End of questions