To find the equation of the perpendicular bisector of the line segment connecting points A(-2,4) and B(4,6), follow these steps:<\/p>\n\n\n\n
Step 1: Find the Midpoint of AB<\/h3>\n\n\n\n
The midpoint formula is: M=(x1+x22,y1+y22)M = \\left( \\frac{x_1 + x_2}{2}, \\frac{y_1 + y_2}{2} \\right)M=(2×1\u200b+x2\u200b\u200b,2y1\u200b+y2\u200b\u200b)<\/p>\n\n\n\n
Substitute the coordinates of A(-2,4) and B(4,6): M=(\u22122+42,4+62)M=(22,102)M=(1,5)M = \\left( \\frac{-2 + 4}{2}, \\frac{4 + 6}{2} \\right) M = \\left( \\frac{2}{2}, \\frac{10}{2} \\right) M = (1, 5)M=(2\u22122+4\u200b,24+6\u200b)M=(22\u200b,210\u200b)M=(1,5)<\/p>\n\n\n\n
So, the midpoint M(1,5)M(1, 5)M(1,5) is on the perpendicular bisector.<\/p>\n\n\n\n
Step 2: Find the Slope of AB<\/h3>\n\n\n\n
The formula for the slope of a line through two points (x\u2081, y\u2081) and (x\u2082, y\u2082) is: m=y2\u2212y1x2\u2212x1m = \\frac{y_2 – y_1}{x_2 – x_1}m=x2\u200b\u2212x1\u200by2\u200b\u2212y1\u200b\u200b<\/p>\n\n\n\n
Substitute the coordinates of A(-2, 4) and B(4, 6): m=6\u221244\u2212(\u22122)=26=13m = \\frac{6 – 4}{4 – (-2)} = \\frac{2}{6} = \\frac{1}{3}m=4\u2212(\u22122)6\u22124\u200b=62\u200b=31\u200b<\/p>\n\n\n\n
So, the slope of line AB is 13\\frac{1}{3}31\u200b.<\/p>\n\n\n\n
Step 3: Find the Slope of the Perpendicular Bisector<\/h3>\n\n\n\n
The slope of the perpendicular bisector is the negative reciprocal of the slope of AB. If the slope of AB is 13\\frac{1}{3}31\u200b, then the slope of the perpendicular bisector will be: mperp=\u22123m_{\\text{perp}} = -3mperp\u200b=\u22123<\/p>\n\n\n\n
Step 4: Use the Point-Slope Form to Find the Equation of the Perpendicular Bisector<\/h3>\n\n\n\n
The point-slope form of a line is: y\u2212y1=m(x\u2212x1)y – y_1 = m(x – x_1)y\u2212y1\u200b=m(x\u2212x1\u200b)<\/p>\n\n\n\n
We know the slope mperp=\u22123m_{\\text{perp}} = -3mperp\u200b=\u22123 and the point on the line M(1,5)M(1, 5)M(1,5). Substituting these values into the point-slope form: y\u22125=\u22123(x\u22121)y – 5 = -3(x – 1)y\u22125=\u22123(x\u22121)<\/p>\n\n\n\n
Simplify: y\u22125=\u22123x+3y – 5 = -3x + 3y\u22125=\u22123x+3<\/p>\n\n\n\n
Add 5 to both sides: y=\u22123x+8y = -3x + 8y=\u22123x+8<\/p>\n\n\n\n
Final Answer:<\/h3>\n\n\n\n
The equation of the perpendicular bisector of AB is: y=\u22123x+8y = -3x + 8y=\u22123x+8<\/p>\n\n\n\n
This is the slope-intercept form of the perpendicular bisector<\/p>\n\n\n\n Write an equation in slope-intercept form for the perpendicular bisector of AB where A(-2,4) and B(4,6) The Correct Answer and Explanation is: To find the equation of the perpendicular bisector of the line segment connecting points A(-2,4) and B(4,6), follow these steps: Step 1: Find the Midpoint of AB The midpoint formula is: M=(x1+x22,y1+y22)M = […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-252467","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/252467","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=252467"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/252467\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=252467"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=252467"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=252467"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-239.jpeg\")
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