The distance formula is derived from the Pythagorean theorem.<\/p>\n\n\n\n
The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n Correct Answer: True<\/strong><\/p>\n\n\n\n The distance formula is indeed derived from the Pythagorean Theorem. The Pythagorean Theorem is a fundamental principle in geometry that states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. It is expressed as: In coordinate geometry, the distance formula is used to determine the distance between two points in a plane. Suppose the two points are (x1,y1)(x\u2081, y\u2081) and (x2,y2)(x\u2082, y\u2082). To find the straight-line distance between them, imagine creating a right triangle by drawing a horizontal and a vertical line to connect the points. The horizontal side of the triangle is the difference in the x-values: x2\u2212x1x\u2082 – x\u2081, and the vertical side is the difference in the y-values: y2\u2212y1y\u2082 – y\u2081.<\/p>\n\n\n\n Applying the Pythagorean Theorem, the distance dd between the two points becomes: Taking the square root of both sides gives the distance formula: This formula is an application of the Pythagorean Theorem in the context of coordinate geometry. It works in two-dimensional space and can be extended to three-dimensional space by including the z-coordinates: Therefore, the distance formula is not only related to the Pythagorean Theorem but is a direct extension of it. It allows the calculation of the exact straight-line distance between any two points in a coordinate plane or space.<\/p>\n","protected":false},"excerpt":{"rendered":" The distance formula is derived from the Pythagorean theorem. The correct answer and explanation is: Correct Answer: True The distance formula is indeed derived from the Pythagorean Theorem. The Pythagorean Theorem is a fundamental principle in geometry that states that in a right triangle, the square of the length of the hypotenuse is equal to […]<\/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-34562","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/34562","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=34562"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/34562\/revisions"}],"predecessor-version":[{"id":34563,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/34562\/revisions\/34563"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=34562"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=34562"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=34562"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
a\u00b2 + b\u00b2 = c\u00b2<\/strong><\/p>\n\n\n\n
d\u00b2 = (x\u2082 – x\u2081)\u00b2 + (y\u2082 – y\u2081)\u00b2<\/strong><\/p>\n\n\n\n
d = \u221a[(x\u2082 – x\u2081)\u00b2 + (y\u2082 – y\u2081)\u00b2]<\/strong><\/p>\n\n\n\n
d = \u221a[(x\u2082 – x\u2081)\u00b2 + (y\u2082 – y\u2081)\u00b2 + (z\u2082 – z\u2081)\u00b2]<\/strong><\/p>\n\n\n\n