Worksheet: Projections

In this worksheet, we will practice finding the projection of a point on a line, that of a line segment on a line, that of a ray on a line, and that of a line on a line.

Q1:

What is the result of projecting a point onto a straight line?

  • Aa ray
  • Ba line segment
  • Ca straight line
  • Da point

Q2:

What is the projection of 𝐷 on 𝐴 𝐶 ?

  • Athe point 𝐷
  • B 𝐷 𝐸
  • C 𝐸 𝐶
  • Dthe point 𝐸

Q3:

Complete: The length of the projection of a line segment onto a line is the length of the line segment itself.

  • Aat most
  • Bat least

Q4:

Determine the length of the projection of 𝐴 𝐵 on 𝐵 𝐶 .

Q5:

Given a triangle 𝐴 𝐵 𝐶 where 𝑚 𝐵 = 9 0 , what is the projection of 𝐶 on 𝐴 𝐵 ?

  • A 𝐵 𝐴
  • B 𝐶 𝐵
  • Cthe point 𝐶
  • Dthe point 𝐵

Q6:

Find the length of the projection of 𝐴 𝐸 on 𝐵 𝐶 .

Q7:

If 𝑋 𝐴 𝐵 , what is the projection of 𝑋 on 𝐴 𝐵 ?

  • A 𝑋 𝐵
  • B 𝐴 𝑋
  • Cthe point 𝐵
  • Dthe point 𝑋

Q8:

Find the projection of the point 𝐴 ( 9 , 2 , 3 ) on the straight line passing through the points 𝐵 ( 1 , 8 , 4 ) and 𝐶 ( 0 , 5 , 6 ) .

  • A ( 0 , 5 , 1 )
  • B ( 1 , 3 , 2 )
  • C ( 1 , 8 , 4 )
  • D ( 0 , 5 , 6 )

Q9:

What is the result of projecting a line segment onto a straight line, given that the two are not perpendicular?

  • Aa point
  • Ba ray
  • Ca straight line
  • Da line segment

Q10:

What can you say about the length of the projection of a line segment onto a straight line, given that the two are perpendicular?

  • AIt is equal to the length of the line segment.
  • BIt is greater than the length of the line segment.
  • CIt is greater than or equal to the length of the line segment.
  • DIt is equal to zero.

Q11:

𝐴 𝐵 is a line segment of length 93 cm, and 𝑋 is a plane. Determine the length of the projection of 𝐴 𝐵 on 𝑋 if 𝐴 𝐵 is parallel to the plane 𝑋 .

Q12:

What is the result of projecting a ray onto a straight line, given that the two are not perpendicular?

  • Aa point
  • Ba line segment
  • Ca straight line
  • Da ray

Q13:

Given that 𝐴 𝐵 = 2 9 , 𝐶 𝐵 = 2 0 , and 𝐶 𝐷 = 3 5 , calculate the length of the projection of 𝐶 𝐷 on 𝐴 𝐷 .

Q14:

What is the projection of 𝐶 𝐷 on 𝐵 𝐷 ?

  • A 𝐶 𝐷
  • B 𝐶 𝑀
  • C 𝐶 𝐵
  • D 𝑀 𝐷

Q15:

What is the projection of 𝐴 on 𝐷 𝐶 ?

  • Athe point 𝐴
  • B 𝐴 𝐵
  • C 𝐵 𝐷
  • Dthe point 𝐵

Q16:

What is the projection of 𝐴 𝐷 on 𝐴 𝐶 ?

  • A 𝐴 𝐷
  • B 𝐷 𝑀
  • C 𝑀 𝐶
  • D 𝐴 𝑀

Q17:

What is the projection of 𝐴 𝐷 on 𝐵 𝐶 ?

  • A 𝐷 𝐵
  • B 𝐴 𝐷
  • Cthe point 𝐴
  • Dthe point 𝐷

Q18:

What is the projection of 𝐴 𝐷 on 𝐶 𝐷 ?

  • A 𝐴 𝐶
  • B 𝐴 𝐷
  • C 𝐴 𝐵
  • D 𝐶 𝐷

Q19:

If 𝐴 𝐵 𝐵 𝐶 , what is the projection of 𝐴 𝐵 on 𝐵 𝐶 ?

  • A 𝐴 𝐵
  • B 𝐵 𝐶
  • Cthe point 𝐶
  • Dthe point 𝐵

Q20:

What is the projection of 𝐶 𝑀 on 𝐴 𝐵 ?

  • A 𝑀 𝐹
  • B 𝐶 𝐹
  • Cthe point 𝑀
  • Dthe point 𝐹

Q21:

What is the projection of 𝐴 𝐷 on 𝐴 𝐶 ?

  • A 𝐴 𝐷
  • B 𝐷 𝐸
  • Cthe point 𝐸
  • D 𝐴 𝐸

Q22:

Find the length of the projection of on .

  • A 22 cm
  • B 18 cm
  • C cm
  • D cm

Q23:

Determine the length of the projection of 𝐴 𝐷 on 𝐵 𝐶 .

Q24:

What is the projection of 𝐴 𝐵 on 𝐴 𝐷 ?

  • A 𝐷 𝐵
  • B 𝐴 𝐵
  • C 𝐶 𝐵
  • D 𝐴 𝐷

Q25:

Find the length of the projection of 𝐵 𝐶 on 𝐷 𝐶 and the area of the trapezium 𝐴 𝐵 𝐶 𝐷 .

  • A 10.5 cm, 842.4 cm2
  • B 20.8 cm, 1,466.4 cm2
  • C 30 cm, 421.2 cm2
  • D 10.5 cm, 733.2 cm2

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