Drawing shapes

Geometry and measures

These are original practice questions, not a past paper. This site is independent and not affiliated with AQA or Pearson.

Plot $A(1, 1)$, $B(4, 1)$ and $C(4, 3)$. Write the coordinates of $D$ so that $ABCD$ is a rectangle with sides parallel to the axes.

2 marks
A triangle has vertices $(0, 0)$, $(4, 0)$ and $(2, 3)$. What special type of triangle is it?

2 marks
A square has two vertices at $(1, 1)$ and $(1, 4)$, and its sides are parallel to the axes. Write both possible pairs of coordinates for the other two vertices.

3 marks
A triangle has vertices $(0, 0)$, $(6, 0)$ and $(0, 6)$. Name the type of triangle and find its area.

Triangle with vertices (0, 0), (6, 0) and (0, 6)

3 marks
A kite has vertices $(2, 0)$, $(0, 3)$, $(2, 6)$ and $(4, 3)$. Write the equation of its line of symmetry, the lengths of both diagonals, and the area.

4 marks
Using a ruler and compasses, construct a triangle with sides $6$ cm, $5$ cm and $4$ cm. Which side is opposite the largest angle?

4 marks
Shape $A$ has vertices $(1, 1)$, $(3, 1)$, $(3, 2)$ and $(1, 2)$. Name the shape and its perimeter. Translate it by $\begin{pmatrix} 4 \\ 2 \end{pmatrix}$ and write the new vertices.

5 marks
An isosceles trapezium has vertices $(0, 0)$, $(8, 0)$, $(6, 3)$ and $(2, 3)$. Show that the non-parallel sides are equal, find the area, and write the equation of the line of symmetry.

Isosceles trapezium

6 marks

Mark scheme

Answer. $D(1, 3)$
- $D$ has the $x$-coordinate of $A$ and the $y$-coordinate of $C$.
- $(1, 3)$
Answer. Isosceles
- The distances from $(2, 3)$ to the two base points are both $\sqrt{13}$.
- Two sides are equal, so the triangle is isosceles.
Answer. $(4, 1)$ and $(4, 4)$, or $(-2, 1)$ and $(-2, 4)$
- The side length is $3$.
- The square can be drawn to the right or to the left.
Answer. Right-angled isosceles, area $18$
- Two sides lie on the axes and are equal, so it is a right-angled isosceles triangle.
- Area $= \dfrac{1}{2} \times 6 \times 6 = 18$.
Answer. Line $x = 2$, diagonals $6$ and $4$, area $12$
- The vertical diagonal lies on $x = 2$ and has length $6$.
- The horizontal diagonal has length $4$.
- Area $= \dfrac{6 \times 4}{2} = 12$.
Answer. The side of length $6$ cm
- Draw one side, then use arcs of the other two lengths from its ends.
- The largest angle is opposite the longest side.
- That side is $6$ cm.
Answer. A $2$ by $1$ rectangle, perimeter $6$. Image: $(5, 3)$, $(7, 3)$, $(7, 4)$, $(5, 4)$.
- The width is $2$ and the height is $1$.
- Perimeter $= 2(2 + 1) = 6$.
- Add $4$ to each $x$-coordinate and $2$ to each $y$-coordinate.
Answer. Both sloping sides are $\sqrt{13}$. Area $18$. The line of symmetry is $x = 4$.
- Left side: $\sqrt{(2 - 0)^{2} + (3 - 0)^{2}} = \sqrt{13}$.
- Right side: $\sqrt{(8 - 6)^{2} + (0 - 3)^{2}} = \sqrt{13}$.
- Area $= \dfrac{8 + 4}{2} \times 3 = 18$.
- The line of symmetry is $x = 4$.