Determine if the following equation has x-axis symmetry; y-axis symmetry, origin symmetry, or none of these 1 =y+1 Answer x-Axis Symmetry O y-Axis Symmetry Origin Symmetry None of these
The Correct Answer and Explanation is:
To determine the symmetry of the equation:
Given Equation:
1=y+11 = y + 11=y+1
Step 1: Simplify the equation
Subtract 1 from both sides:1−1=y+1−1⇒0=y1 – 1 = y + 1 – 1 \Rightarrow 0 = y1−1=y+1−1⇒0=y
So, the equation simplifies to:y=0y = 0y=0
This is a horizontal line along the x-axis.
Step 2: Test for different types of symmetry
a) x-axis symmetry:
To test for x-axis symmetry, replace yyy with −y-y−y in the equation and see if the equation remains unchanged.y=0⇒−y=0⇒y=0y = 0 \Rightarrow -y = 0 \Rightarrow y = 0y=0⇒−y=0⇒y=0
The equation remains the same. So, it has x-axis symmetry.
b) y-axis symmetry:
To test for y-axis symmetry, replace xxx with −x-x−x. However, this equation does not contain xxx, so replacing xxx does not affect the equation. Thus, the equation remains unchanged under this transformation.
So, the equation has y-axis symmetry.
c) Origin symmetry:
To test for origin symmetry, replace both xxx with −x-x−x and yyy with −y-y−y.
Again, since there is no xxx in the equation, and yyy is zero, replacing it with −y-y−y still gives y=0y = 0y=0. The equation remains unchanged.
So, the equation has origin symmetry.
Final Answer:
✅ x-axis symmetry
✅ y-axis symmetry
✅ origin symmetry
However, based on standard multiple-choice conventions, you must choose the most specific applicable symmetry. Since it has all three, the best choice depends on the options allowed.
But if the answer choices are mutually exclusive as in:
- x-axis symmetry
- y-axis symmetry
- origin symmetry
- none of these
Then the correct answer is:
✅ x-axis symmetry (since it lies on the x-axis, which directly indicates x-axis symmetry)
