Parallel and perpendicular linesEdexcel International A Level Maths: Subtopic test

1. 1
   The line $l_1$ has equation $2x+5y=10$.

   (a)

   Find the gradient of a line that is perpendicular to $l_1$.

   [1 mark]

   • A$-\frac52$
   • B$\frac25$
   • C$\frac52$
   • D$-\frac25$

   (b)

   Which of the following lines is parallel to $l_1$?

   [1 mark]

   • A$4x+10y=7$
   • B$5x+2y=10$
   • C$2x-5y=10$
   • D$5x-2y=10$

   (c)

   Find an equation of the line parallel to $l_1$ that passes through the point $(5,-1)$.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   The line $l_2$ passes through the points $A(1,2)$ and $B(5,10)$.

   (a)

   Find the gradient of a line perpendicular to $l_2$.

   [1 mark]

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

   (b)

   Which of the following lines is perpendicular to $l_2$?

   [1 mark]

   • A$y=2x+3$
   • B$x+2y=11$
   • C$2x-y=4$
   • D$2x+y=1$

   (c)

   Find an equation of the line through $A$ that is perpendicular to $l_2$, giving your answer in the form $ax+by+c=0$ with integer $a$, $b$ and $c$.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   The line $l$ has equation $4x+3y=24$. It passes through the points $A(6,0)$ and $B(0,8)$.

   (a)

   Find an equation of the line through $A$ that is perpendicular to $l$, giving your answer in the form $ax+by+c=0$ with integer $a$, $b$ and $c$.

   [3 marks]

   (b)

   The line through $B$ that is perpendicular to $l$ meets the $x$-axis at $C$. Find the coordinates of $C$ and the area of triangle $ABC$.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   The points $A(0,4)$, $B(6,0)$ and $C(8,3)$ are three vertices of a quadrilateral $ABCD$.

   (a)

   (i) Show that angle $ABC$ is a right angle.
   (ii) Find an equation of the line through $C$ that is parallel to $AB$, in the form $ax+by+c=0$ with integer $a$, $b$ and $c$.

   [6 marks]

   (b)

   The point $D$ is such that $ABCD$ is a rectangle. Find the coordinates of $D$, and find an equation of the line through $D$ that is perpendicular to the diagonal $AC$.

   [6 marks]

   Total for question 4: 12 marks

End of questions