Perpendicular to a given line through a given point | Maths

Starter quiz

This quadrilateral is a kite. Find the value of angle $a$ , in degrees.
- '100' ✓
This diagram shows an accurate construction of a perpendicular bisector. YZ has a length of 8.4 cm. Which of these is the smallest value of $r$ that can be used in this construction?
- 2.1 cm
- 4.3 cm ✓
- 8.4 cm
- 16.8 cm
- 8.4 $\pi$ cm
Match the sentence to the diagram.
- a
  
  ⇔
  
  A bisector to line segment QV ✓
- b
  
  ⇔
  
  A perpendicular to line segment QV ✓
- c
  
  ⇔
  
  A perpendicular bisector to line segment QV ✓
- d
  
  ⇔
  
  An intersecting line to line segment QV ✓
This is an incomplete construction to find the perpendicular bisector of YZ. Which of these steps is missing from this construction?
- A circle with centre at point Y.
- A line segment connecting the intersection to point Z.
- An arc below YZ with centre at point Z. ✓
- An arc above YZ with centre at point Z.
- A line through two pairs of intersecting arcs. ✓
This is an accurate construction to draw a rhombus. What is the perimeter (in cm) of the rhombus that can be drawn from this construction?
- '56' ✓
Sofia starts her construction of a perpendicular bisector to EF. She is about to move the pair of compoasses to construct a second circle. Which of these statements are true?
- Sofia needs to place the compass needle at the midpoint of EF.
- Sofia should draw a circle with centre at the intersection of EF and the circle.
- Sofia needs to draw an arc with centre at point F next.
- Sofia should adjust the compass width so that both circles drawn are congruent. ✓
- Currently, the next circle Sofia draws will be smaller than the first. ✓