{"id":639740,"date":"2023-06-26T06:55:57","date_gmt":"2023-06-26T01:25:57","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/determine-graphically-the-vertices-of-a-triangle-the-equations-of-whose-sides-are-given-as-follows-2y-x8-5y-x14-and-2xy1\/"},"modified":"2025-06-26T12:47:25","modified_gmt":"2025-06-26T07:17:25","slug":"determine-graphically-the-vertices-of-a-triangle-the-equations-of-whose-sides-are-given-as-follows-2y-x8-5y-x14-and-2xy1","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/determine-graphically-the-vertices-of-a-triangle-the-equati\/","title":{"rendered":"Determine graphically the vertices of a triangle, the equations of whose sides are given as follows: 2y-x=8, 5y-x=14 and -2x+y=1."},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Determine graphically the vertices of a triangle, the equations of whose sides are given as follows: 2y-x=8, 5y-x=14 and -2x+y=1.","custom_permalink":"question\/mathematics\/determine-graphically-the-vertices-of-a-triangle-the-equati\/"},"categories":[],"acf":{"question":"

Determine graphically the vertices of a triangle, the equations of whose sides are given as follows: 2y-x=8, 5y-x=14 and -2x+y=1.<\/span><\/p>

<\/p>

<\/p><\/spanstyle=\"-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:0pt;line-height:normal\"><\/spanstyle=\"-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:0pt;line-height:normal\">","options":[{"option":"(-4, 2), (1, 3) and (2, 5)","correct":true},{"option":"(-2, 4), (1, 3) and (2, 5)","correct":false},{"option":"(-4, 2), (-1, 3) and (2, 5)","correct":false},{"option":"None of these <\/span>","correct":false}],"solution":"Give pair of linear equations <\/span>\r\n\r\n \r\n \r\n 2<\/m:mn>y<\/m:mi>\u2212<\/m:mo>x<\/m:mi>=<\/m:mo>8<\/m:mn>\u2003<\/m:mtext>\u2026<\/m:mo>\u2026<\/m:mo>.<\/m:mo>(<\/m:mo>1<\/m:mn>)<\/m:mo>,<\/m:mo>\u2003<\/m:mtext>5<\/m:mn>y<\/m:mi>\u2212<\/m:mo>x<\/m:mi>=<\/m:mo>14<\/m:mn>\u2003<\/m:mtext>\u2026<\/m:mo>\u2026<\/m:mo>.<\/m:mo>(<\/m:mo>2<\/m:mn>)<\/m:mo><\/m:mrow>\r\n <\/m:semantics><\/math>  and <\/span>\r\n\r\n \r\n \r\n \u2212<\/m:mo>2<\/m:mn>x<\/m:mi>+<\/m:mo>y<\/m:mi>=<\/m:mo>1<\/m:mn><\/m:mrow>\r\n <\/m:semantics><\/math> .......... (3) <\/span>
To find the vertices of a triangle graphically, we will solve the equations in any one variable and make the table for the values of coordinates.<\/span>
Solving the equation (1), writing y in terms of x and making the table for the co-ordinates. <\/span>
2y=8+x <\/span>
\u21d2<\/mo>y<\/mi>=<\/mo>8<\/mn>+<\/mo>x<\/mi><\/mrow>2<\/mn><\/mrow><\/mfrac><\/math>

x<\/span><\/p><\/td>

y<\/span><\/p><\/td><\/tr>

-4<\/span><\/p><\/td>

2<\/span><\/p><\/td><\/tr>

2<\/span><\/p><\/td>

5<\/span><\/p><\/td><\/tr><\/tbody><\/table>Solving the equation (2), write in y terms and make the table for the co-ordinates. <\/span>
\u21d2<\/mo>5<\/mn>y<\/mi>-<\/mo>x<\/mi>=<\/mo>14<\/mn><\/math>
\u21d2<\/mo>y<\/mi>=<\/mo>14<\/mn>+<\/mo>x<\/mi><\/mrow>5<\/mn><\/mrow><\/mfrac><\/math>

x<\/span><\/p><\/td>

y<\/span><\/p><\/td><\/tr>

1<\/span><\/p><\/td>

3<\/span><\/p><\/td><\/tr>

-4<\/span><\/p><\/td>

2<\/span><\/p><\/td><\/tr><\/tbody><\/table>Solving the equation (3), write in y terms and make the table for the co-ordinates. <\/span>
\u21d2<\/mo>-<\/mo>2<\/mn>x<\/mi>+<\/mo>y<\/mi>=<\/mo>1<\/mn><\/math>
\u21d2<\/mo>y<\/mi>=<\/mo>1<\/mn>+<\/mo>2<\/mn>x<\/mi><\/math>

x<\/span><\/p><\/td>

y<\/span><\/p><\/td><\/tr>

1<\/span><\/p><\/td>

0<\/span><\/p><\/td><\/tr>

2<\/span><\/p><\/td>

5<\/span><\/p><\/td><\/tr><\/tbody><\/table>Plotting all the points on the graph.<\/span>
\"\"From the graph, it is observed that the lines taken in pairs intersect each other at points A(-4,2), B(1,3) and C(2,5). <\/span>
Hence, the vertices of the triangle ABC are A(-4,2), B(1,3) and C(2,5).<\/span>
Hence, option (1) is correct.<\/span>
 <\/span>","subject":"Mathematics"},"yoast_head":"\nDetermine graphically the vertices of a triangle, the equations of whose sides are given as follows: 2y-x=8, 5y-x=14 and -2x+y=1. - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"Determine graphically the vertices of a triangle, the equations of whose sides are given as follows: 2y-x=8, 5y-x=14 and -2x+y=1.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/determine-graphically-the-vertices-of-a-triangle-the-equati\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Determine graphically the vertices of a triangle, the equations of whose sides are given as follows: 2y-x=8, 5y-x=14 and -2x+y=1. - Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"og:description\" content=\"Determine graphically the vertices of a triangle, the equations of whose sides are given as follows: 2y-x=8, 5y-x=14 and -2x+y=1.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/determine-graphically-the-vertices-of-a-triangle-the-equati\/\" \/>\n<meta property=\"og:site_name\" content=\"Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/\" \/>\n<meta property=\"article:modified_time\" content=\"2025-06-26T07:17:25+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2025\/04\/infinitylearn.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1920\" \/>\n\t<meta property=\"og:image:height\" content=\"1008\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:site\" content=\"@InfinityLearn_\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Determine graphically the vertices of a triangle, the equations of whose sides are given as follows: 2y-x=8, 5y-x=14 and -2x+y=1. - 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