Grade 11 Math: Projections Worksheet

Grade 11 Math: Projections

Read each question carefully and provide your answers in the space provided. Show all your work for full credit.

1. The   of a point onto a line is the foot of the perpendicular from the point to the line.

2. An   projection is a projection in which the projectors are perpendicular to the projection plane.

3. The projection of a line segment onto a line can be a point or a  .

4. Given a point P(3, 4) and a line L defined by the equation y = x. Find the coordinates of the orthogonal projection of P onto L.

5. Consider a line segment AB with A(1, 5) and B(7, 1). Find the length of the orthogonal projection of AB onto the x-axis.

6. What is the projection of a point onto a plane?

7. If a line is parallel to the projection plane, its orthogonal projection will be:

8. The projection of a circle onto a plane is always a circle.

9. The length of the projection of a vector onto another vector can be negative.

10. A vector \(\vec{a} = \begin{pmatrix} 4 \\ 3 \end{pmatrix}\) is projected onto the vector \(\vec{b} = \begin{pmatrix} 1 \\ 0 \end{pmatrix}\). Find the scalar projection of \(\vec{a}\) onto \(\vec{b}\) and the vector projection of \(\vec{a}\) onto \(\vec{b}\).

11. Consider a square ABCD in the xy-plane with vertices A(0,0), B(4,0), C(4,4), and D(0,4). Draw the square and its orthogonal projection onto the line y=x. Label the projected vertices.