Worksheet: Projections

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

Q1:

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

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

Q2:

What is the projection of 𝐷 on 𝐴𝐶?

  • A𝐷𝐸
  • B𝐸𝐶
  • Cthe point 𝐷
  • 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 least
  • Bat most

Q4:

Determine the length of the projection of 𝐴𝐵 on 𝐵𝐶.

Q5:

Given a triangle 𝐴𝐵𝐶 where 𝑚𝐵=90, what is the projection of 𝐶 on 𝐴𝐵?

  • A𝐵𝐴
  • Bthe point 𝐶
  • C𝐶𝐵
  • Dthe point 𝐵

Q6:

Find the length of the projection of 𝐴𝐸 on 𝐵𝐶.

Q7:

If 𝑋𝐴𝐵, what is the projection of 𝑋 on 𝐴𝐵?

  • Athe point 𝐵
  • B𝑋𝐵
  • Cthe point 𝑋
  • D𝐴𝑋

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

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 line segment
  • Da straight line

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 greater than the length of the line segment.
  • BIt is equal to 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:

𝐴𝐵 is a line segment of length 93 cm, and 𝑋 is a plane. Determine the length of the projection of 𝐴𝐵 on 𝑋 if 𝐴𝐵 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 straight line
  • Ba ray
  • Ca line segment
  • Da point

Q13:

Given that 𝐴𝐵=29, 𝐶𝐵=20, and 𝐶𝐷=35, calculate the length of the projection of 𝐶𝐷 on 𝐴𝐷.

Q14:

What is the projection of 𝐶𝐷 on 𝐵𝐷?

  • A𝐶𝐷
  • B𝐶𝑀
  • C𝑀𝐷
  • D𝐶𝐵

Q15:

What is the projection of 𝐴 on 𝐷𝐶?

  • Athe point 𝐵
  • B𝐵𝐷
  • Cthe point 𝐴
  • D𝐴𝐵

Q16:

What is the projection of 𝐴𝐷 on 𝐴𝐶?

  • A𝐷𝑀
  • B𝐴𝑀
  • C𝑀𝐶
  • D𝐴𝐷

Q17:

What is the projection of 𝐴𝐷 on 𝐵𝐶?

  • A𝐴𝐷
  • B𝐷𝐵
  • Cthe point𝐷
  • Dthe point𝐴

Q18:

What is the projection of 𝐴𝐷 on 𝐶𝐷?

  • A𝐴𝐷
  • B𝐴𝐵
  • C𝐴𝐶
  • D𝐶𝐷

Q19:

If 𝐴𝐵𝐵𝐶, what is the projection of 𝐴𝐵 on 𝐵𝐶?

  • Athe point 𝐶
  • B𝐵𝐶
  • C𝐴𝐵
  • Dthe point 𝐵

Q20:

What is the projection of 𝐶𝑀 on 𝐴𝐵?

  • A𝐶𝐹
  • Bthe point 𝐹
  • Cthe point 𝑀
  • D𝑀𝐹

Q21:

What is the projection of 𝐴𝐷 on 𝐴𝐶?

  • A𝐴𝐷
  • B𝐷𝐸
  • Cthe point 𝐸
  • D𝐴𝐸

Q22:

Find the length of the projection of 𝑀𝐸 on 𝑀𝐷.

  • A18 cm
  • B2481 cm
  • C2643 cm
  • D22 cm

Q23:

Determine the length of the projection of 𝐴𝐷 on 𝐵𝐶.

Q24:

What is the projection of 𝐴𝐵 on 𝐴𝐷?

  • A𝐴𝐷
  • B𝐴𝐵
  • C𝐷𝐵
  • D𝐶𝐵

Q25:

Find the length of the projection of 𝐵𝐶 on 𝐷𝐶 and the area of the trapezoid 𝐴𝐵𝐶𝐷.

  • A20.8 cm, 1,466.4 cm2
  • B10.5 cm, 842.4 cm2
  • C10.5 cm, 733.2 cm2
  • D30 cm, 421.2 cm2

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