Question

use the figure below to complete parts (a) through (d).
(a) find the image of p under the reflection with axis \\(l_1\\).
the point is the reflection of p across axis \\(l_1\\).

Explanation:

Identify the coordinates of point P

Let the intersection of the main axes \(L_1\) (horizontal axis) and \(L_2\) (vertical axis) be the origin \((0,0)\).
Each grid square represents 1 unit.
Point \(P\) is located 3 units to the right of \(L_2\) and 4 units above \(L_1\).
Thus, the coordinates of \(P\) are \((3, 4)\).

Identify the reflection axis

The reflection axis is \(L_1\), which is the horizontal axis (the x-axis).

Apply the reflection rule

Reflecting a point \((x, y)\) across the horizontal axis \(L_1\) (the x-axis) negates its y-coordinate:

$$ (x, y) ightarrow (x, -y) $$

Applying this to \(P(3, 4)\):

$$ (3, 4) ightarrow (3, -4) $$

Locate the reflected point on the grid

We look for the labeled point at coordinates \((3, -4)\), which is 3 units to the right of \(L_2\) and 4 units below \(L_1\).
Looking at the grid, point \(C\) is located at \((3, -4)\).
Therefore, the reflection of \(P\) across axis \(L_1\) is \(C\).

Answer:

(a) Find the image of P under the reflection with axis \(L_1\).

The point <blank>C</blank> is the reflection of P across axis \(L_1\).