Midpoint and distance between two pointsIB MYP Maths Extended: Subtopic test

1. 1
   On a map of an island, a straight path runs from a lighthouse at $A(-2, 3)$ to a jetty at $B(6, 7)$. One unit on the grid represents 1 km.

   (a)

   Find the midpoint of $AB$.

   [1 mark]

   • A$(4, 10)$
   • B$(2, 5)$
   • C$(4, 2)$
   • D$(-1, 1.5)$

   (b)

   Find the gradient of the line $AB$.

   [1 mark]

   • A$2$
   • B$-\frac{1}{2}$
   • C$\frac{1}{2}$
   • D$1$

   (c)

   Find the exact length of the path $AB$.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A triangular garden has its corners at $P(1, 1)$, $Q(7, 1)$ and $R(4, 5)$ on a plan where one unit represents 1 m.

   (a)

   Find the gradient of the side $PR$.

   [1 mark]

   • A$\frac{4}{3}$
   • B$\frac{3}{4}$
   • C$\frac{4}{5}$
   • D$-\frac{4}{3}$

   (b)

   Which statement about triangle $PQR$ is correct?

   [1 mark]

   • AIt is equilateral, because $PQ$ is horizontal.
   • BIt is right-angled at $R$.
   • CIt is scalene, because $PQ$ is longer than the other sides.
   • DIt is isosceles, because $PR=QR$.

   (c)

   Find the area of the garden.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A quadrilateral $ABCD$ is drawn on a coordinate grid with $A(0, 0)$, $B(4, 3)$, $C(7, -1)$ and $D(3, -4)$.

   (a)

   Find the lengths of $AB$ and $BC$.

   [3 marks]

   (b)

   You are given that $CD=DA=5$. Find the exact length of $AC$. Hence show that angle $ABC$ is a right angle and name the quadrilateral.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A delivery drone flies in a straight line from a depot at $D(2, 1)$ to a school at $S(14, 6)$, where one unit represents 1 km. It flies at a constant speed of $26$ km/h.

   (a)

   (i) Find the coordinates of the midpoint $M$ of $DS$, where the drone drops a parcel.
   (ii) Find the exact distance $DS$.
   (iii) Find the time the drone takes to fly from $D$ to $S$, in minutes.

   [6 marks]

   (b)

   A second school $T$ is at $(26, 11)$. A pilot suggests that the drone could fly from $D$ straight to $T$ over $S$. Justify whether $S$ lies on the straight line $DT$, and find the length of $DT$.

   [6 marks]

   Total for question 4: 12 marks

End of questions