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Lesson: Projections

In this lesson, we will learn how to find 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.

Sample Question Videos

01:01

Worksheet • 25 Questions • 1 Video

Q1:

Determine the length of the projection of 𝐴 𝐡 on 𝐡 𝐢 .

Q2:

𝐴 𝐡 is a line segment of length 93 cm, and 𝑋 is a plane. Determine the length of the projection of 𝐴 𝐡 on 𝑋 if βƒ–     βƒ— 𝐴 𝐡 is parallel to the plane 𝑋 .

Q3:

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

  • Aat least
  • Bat most

Q4:

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

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

Q5:

Find the length of the projection of 𝐴 𝐸 on βƒ–     βƒ— 𝐡 𝐢 .

Q6:

Given that 𝐴 𝐡 = 2 9 , 𝐢 𝐡 = 2 0 , and 𝐢 𝐷 = 3 5 , calculate the length of the projection of 𝐢 𝐷 on βƒ–      βƒ— 𝐴 𝐷 .

Q7:

Determine the length of the projection of 𝐴 𝐷 on βƒ–     βƒ— 𝐡 𝐢 .

Q8:

Find the length of the projection of on .

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

Q9:

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

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

Q10:

What is the projection of 𝐢 𝐷 on βƒ–     βƒ— 𝐡 𝐷 ?

  • A 𝑀 𝐷
  • B 𝐢 𝑀
  • C 𝐢 𝐡
  • D 𝐢 𝐷

Q11:

What is the projection of 𝐴 on βƒ–     βƒ— 𝐷 𝐢 ?

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

Q12:

If 𝑋 ∈ βƒ–     βƒ— 𝐴 𝐡 , what is the projection of 𝑋 on βƒ–     βƒ— 𝐴 𝐡 ?

  • Athe point 𝑋
  • B 𝐴 𝑋
  • Cthe point 𝐡
  • D 𝑋 𝐡

Q13:

Given a triangle 𝐴 𝐡 𝐢 where π‘š ∠ 𝐡 = 9 0 ∘ , what is the projection of 𝐢 on βƒ–     βƒ— 𝐴 𝐡 ?

  • Athe point 𝐡
  • B 𝐢 𝐡
  • Cthe point 𝐢
  • D 𝐡 𝐴

Q14:

What is the projection of 𝐴 𝐷 on βƒ–     βƒ— 𝐴 𝐢 ?

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

Q15:

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

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

Q16:

Find the length of the projection of 𝐡 𝐢 on βƒ–     βƒ— 𝐷 𝐢 and the area of the trapezium 𝐴 𝐡 𝐢 𝐷 .

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

Q17:

What is the projection of 𝐴 𝐷 on βƒ–     βƒ— 𝐡 𝐢 ?

  • Athe point 𝐷
  • B 𝐴 𝐷
  • Cthe point 𝐴
  • D 𝐷 𝐡

Q18:

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

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

Q19:

What is the projection of 𝐴 𝐷 on βƒ–     βƒ— 𝐢 𝐷 ?

  • A 𝐢 𝐷
  • B 𝐴 𝐷
  • C 𝐴 𝐡
  • D 𝐴 𝐢

Q20:

What is the projection of 𝐷 on βƒ–     βƒ— 𝐴 𝐢 ?

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

Q21:

If 𝐴 𝐡 βŸ‚ 𝐡 𝐢 , what is the projection of 𝐴 𝐡 on βƒ–     βƒ— 𝐡 𝐢 ?

  • Athe point 𝐡
  • B 𝐡 𝐢
  • Cthe point 𝐢
  • D 𝐴 𝐡

Q22:

What is the projection of 𝐢 𝑀 on βƒ–     βƒ— 𝐴 𝐡 ?

  • Athe point 𝐹
  • B 𝐢 𝐹
  • Cthe point 𝑀
  • D 𝑀 𝐹

Q23:

What is the projection of 𝐴 𝐷 on βƒ–     βƒ— 𝐴 𝐢 ?

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

Q24:

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 zero.
  • 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 the length of the line segment.

Q25:

What is the projection of 𝐴 𝐡 on βƒ–      βƒ— 𝐴 𝐷 ?

  • A 𝐴 𝐷
  • B 𝐴 𝐡
  • C 𝐢 𝐡
  • D 𝐷 𝐡
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