What is the reflection of point P (-1 6) on the line x = 1?

Solution:

Given point is (-1, 6)

Let Pꞌ(h, k) be the reflection on the line x = 1.

Now midpoint of PPꞌ = [(h - 1) / 2 , (k + 6) / 2]

Since this point lies on the vertical line (given x =1),

⇒ (h - 1) / 2 = 1

h - 1 = 2

h = 3

Also, PPꞌ is parallel to the x-axis, y-coordinate of P and Pꞌ must be the same.

∴ k = 6

∴ The required image of point P(-1, 6) is Pꞌ(3, 6).

Aliter

Image (h, k) of the point (x₁, y₁) on line Ax + By + C = 0 is given by,

(h - x₁) / A = (k - y₁) / B = -2[Ax₁ + By₁ + C] / (A² + B²) ------(1)

Here, (x₁ , y₁) = (-1, 6) 

⇒ x - 1 = 0

⇒A = 1, B = 0, C = -1

Substituting these values in equation(1)

(h + 1) / 1 = (k - 6) / 0 = -2[-1 - 1] / 1 = 4

⇒ (h + 1) /1 = 4 and (k - 6) / 0 = 4

⇒ h = 3 and k = 6

∴ The image is (3, 6).

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What is the reflection of point P (-1 6) on the line x = 1?

Summary:

The reflection of point P (-1 6) on the line x = 1 is (3, 6).