Projection Math Example 1

Follow the full solution, then compare it with the other examples linked below.

medium

Find the orthogonal projection of point

P(3, 7)

onto the

x

-axis, the

y

-axis, and the line

y = x

1
Step 1: Projection onto the $x$ -axis: drop a perpendicular to the $x$ -axis. The image is $(3, 0)$ .
2
Step 2: Projection onto the $y$ -axis: drop a perpendicular to the $y$ -axis. The image is $(0, 7)$ .
3
Step 3: Projection onto $y = x$ : the projection of $(x_0, y_0)$ onto $y = x$ is $\left(\dfrac{x_0+y_0}{2}, \dfrac{x_0+y_0}{2}\right) = \left(5, 5\right)$ .

Answer

Onto

x

-axis:

(3, 0)

; onto

y

-axis:

(0, 7)

; onto

y = x

(5, 5)

Orthogonal projection drops a perpendicular from the point to the target line. The projection onto

y=x

uses the formula where the projected point lies on the line at the foot of the perpendicular from

P

About Projection

The image formed when points of a shape are mapped onto a lower-dimensional surface along parallel or converging rays.

Vector [formula] is projected onto vector [formula]. Find (a) the scalar projection and (b) the vect

A [formula] m flagpole stands vertically. At [formula] pm the sun casts a horizontal shadow [formula

Project the vector [formula] onto the unit vector [formula] (the [formula]-axis direction). Interpre