{"id":31529,"date":"2025-06-22T03:45:22","date_gmt":"2025-06-22T03:45:22","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=31529"},"modified":"2025-06-22T03:45:25","modified_gmt":"2025-06-22T03:45:25","slug":"determine-if-the-following-equation-has-x-axis-symmetry-y-axis-symmetry-origin-symmetry-or-none-of-these","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/determine-if-the-following-equation-has-x-axis-symmetry-y-axis-symmetry-origin-symmetry-or-none-of-these\/","title":{"rendered":"Determine if the following equation has x-axis symmetry; y-axis symmetry, origin symmetry, or none of these"},"content":{"rendered":"\n

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<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To determine the symmetry of the equation:<\/p>\n\n\n\n

Given Equation:<\/strong>
1=y+11 = y + 11=y+1<\/p>\n\n\n\n

Step 1: Simplify the equation<\/h3>\n\n\n\n

Subtract 1 from both sides:1\u22121=y+1\u22121\u21d20=y1 – 1 = y + 1 – 1 \\Rightarrow 0 = y1\u22121=y+1\u22121\u21d20=y<\/p>\n\n\n\n

So, the equation simplifies to:y=0y = 0y=0<\/p>\n\n\n\n

This is a horizontal line<\/strong> along the x-axis<\/strong>.<\/p>\n\n\n\n

\n\n\n\n

Step 2: Test for different types of symmetry<\/h3>\n\n\n\n

a) x-axis symmetry:<\/strong>
To test for x-axis symmetry, replace yyy with \u2212y-y\u2212y in the equation and see if the equation remains unchanged.y=0\u21d2\u2212y=0\u21d2y=0y = 0 \\Rightarrow -y = 0 \\Rightarrow y = 0y=0\u21d2\u2212y=0\u21d2y=0<\/p>\n\n\n\n

The equation remains the same. So, it has x-axis symmetry<\/strong>.<\/p>\n\n\n\n

b) y-axis symmetry:<\/strong>
To test for y-axis symmetry, replace xxx with \u2212x-x\u2212x. However, this equation does not contain<\/strong> xxx, so replacing xxx does not affect the equation. Thus, the equation remains unchanged under this transformation.<\/p>\n\n\n\n

So, the equation has y-axis symmetry<\/strong>.<\/p>\n\n\n\n

c) Origin symmetry:<\/strong>
To test for origin symmetry, replace both xxx with \u2212x-x\u2212x and yyy with \u2212y-y\u2212y.<\/p>\n\n\n\n

Again, since there is no xxx in the equation, and yyy is zero, replacing it with \u2212y-y\u2212y still gives y=0y = 0y=0. The equation remains unchanged.<\/p>\n\n\n\n

So, the equation has origin symmetry<\/strong>.<\/p>\n\n\n\n

\n\n\n\n

Final Answer:<\/h3>\n\n\n\n

\u2705 x-axis symmetry<\/strong>
\u2705 y-axis symmetry<\/strong>
\u2705 origin symmetry<\/strong><\/p>\n\n\n\n

However, based on standard multiple-choice conventions<\/strong>, you must choose the most specific applicable symmetry<\/strong>. Since it has all three<\/strong>, the best choice depends on the options allowed.<\/p>\n\n\n\n

But if the answer choices are mutually exclusive as in:<\/p>\n\n\n\n

    \n
  • x-axis symmetry<\/li>\n\n\n\n
  • y-axis symmetry<\/li>\n\n\n\n
  • origin symmetry<\/li>\n\n\n\n
  • none of these<\/li>\n<\/ul>\n\n\n\n

    Then the correct answer is:<\/strong><\/p>\n\n\n\n

    \u2705 x-axis symmetry<\/strong> (since it lies on the x-axis, which directly indicates x-axis symmetry)<\/p>\n\n\n\n

    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    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 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-31529","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/31529","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=31529"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/31529\/revisions"}],"predecessor-version":[{"id":31531,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/31529\/revisions\/31531"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=31529"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=31529"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=31529"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}