Math Problem Statement

1. Tentukan bayangan titik A(2, -5) oleh pencerminan terhadap garis y = -x 2. Berapakah hasil refleksi atau pencerminan bidang datar dari titik (3, 5) terhadap sumbu y? 3. Bayangan titik A(2, 5) yang direfleksikan terhadap sumbu y adalah?

Solution

Let's solve the problems step by step based on the questions shown in the image:


1. Tentukan bayangan titik A(2,5)A(2, -5) oleh pencerminan terhadap garis y=xy = -x

  • Solution: The reflection of a point (x,y)(x, y) over the line y=xy = -x is given by swapping and negating both coordinates: (y,x)(-y, -x).

    So for A(2,5)A(2, -5): Reflection of A(2,5) over y=x=(5,2)\text{Reflection of } A(2, -5) \text{ over } y = -x = (5, -2)

    Answer: The reflection of point A(2,5)A(2, -5) is (5,2)(5, -2).


2. Berapakah hasil refleksi atau pencerminan bidang datar dari titik (3,5)(3, 5) terhadap sumbu y?

  • Solution: The reflection of a point (x,y)(x, y) over the yy-axis is done by changing the sign of the xx-coordinate while keeping the yy-coordinate the same. So for (3,5)(3, 5): Reflection over y axis=(3,5)\text{Reflection over } y \text{ axis} = (-3, 5)

    Answer: The reflection of point (3,5)(3, 5) over the yy-axis is (3,5)(-3, 5).


3. Bayangan titik A(2,5)A(2, 5) yang direfleksikan terhadap sumbu y adalah

  • Solution: Similar to question 2, the reflection over the yy-axis is achieved by changing the sign of the xx-coordinate: Reflection of A(2,5) over the y axis=(2,5)\text{Reflection of } A(2, 5) \text{ over the } y \text{ axis} = (-2, 5)

    Answer: The reflection of point A(2,5)A(2, 5) over the yy-axis is (2,5)(-2, 5).


Would you like further details on any of the solutions, or do you have any questions? Here are some related questions to expand your understanding:

  1. How do you reflect a point over the line y=xy = x?
  2. What is the reflection of point (4,3)(4, -3) over the xx-axis?
  3. How do you find the reflection of a point over a generic line y=mx+cy = mx + c?
  4. What is the reflection of point (2,3)(-2, -3) over the origin?
  5. Can a reflection result in the same point in any scenario?

Tip: When reflecting over the y=xy = -x line, always remember to swap and negate the coordinates!

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Math Problem Analysis

Mathematical Concepts

Geometry
Reflection
Coordinate Geometry

Formulas

Reflection over line y = -x: (x, y) → (-y, -x)
Reflection over y-axis: (x, y) → (-x, y)

Theorems

Reflection Theorem

Suitable Grade Level

Grades 7-9