{"id":307024,"date":"2022-09-10T23:43:43","date_gmt":"2022-09-10T18:13:43","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/if-the-ends-of-the-base-of-an-isosceles-triangle-are-at-20-and-01-and-the-equation-of-one-side-is-x2-then-the-orthocenter-of-the-triangle-is\/"},"modified":"2025-06-26T12:21:27","modified_gmt":"2025-06-26T06:51:27","slug":"if-the-ends-of-the-base-of-an-isosceles-triangle-are-at-20-and-01-and-the-equation-of-one-side-is-x2-then-the-orthocenter-of-the-triangle-is","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/if--the-ends-of-the-base-of-an-isosceles-triangle-are-at-2\/","title":{"rendered":"If the ends of the base of an isosceles triangle are at (2,0) and (0,1) and the equation of one side is x=2 \u00a0then the orthocenter of the triangle is"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"If the ends of the base of an isosceles triangle are at (2,0) and (0,1) and the equation of one side is x=2 \u00a0then the orthocenter of the triangle is","custom_permalink":"question\/mathematics\/if--the-ends-of-the-base-of-an-isosceles-triangle-are-at-2\/"},"categories":[],"acf":{"question":"

If the ends of the base of an isosceles triangle are at (<\/mo>2<\/mn>,<\/mo>0<\/mn><\/mrow>)<\/mo><\/mrow><\/mrow><\/math> <\/xml>and (<\/mo>0<\/mn>,<\/mo>1<\/mn><\/mrow>)<\/mo><\/mrow><\/mrow><\/math> <\/xml>and the equation of one side is x<\/mi>=<\/mo>2<\/mn><\/mrow><\/math> <\/xml> then the orthocenter of the triangle is <\/p>","options":[{"option":"

(<\/mo>3<\/mn>\/<\/mo>2<\/mn>,<\/mo>3<\/mn>\/<\/mo>2<\/mn><\/mrow>)<\/mo><\/mrow><\/mrow><\/math> <\/xml> <\/p>","correct":false},{"option":"

(<\/mo>5<\/mn>\/<\/mo>4<\/mn>,<\/mo>1<\/mn><\/mrow>)<\/mo><\/mrow><\/mrow><\/math> <\/xml> <\/p>","correct":true},{"option":"

(<\/mo>3<\/mn>\/<\/mo>4<\/mn>,<\/mo>1<\/mn><\/mrow>)<\/mo><\/mrow><\/mrow><\/math> <\/xml> <\/p>","correct":false},{"option":"

(<\/mo>4<\/mn>\/<\/mo>3<\/mn>,<\/mo>7<\/mn>\/<\/mo>12<\/mn><\/mrow>)<\/mo><\/mrow><\/mrow><\/math> <\/xml> <\/p>","correct":false}],"solution":"

Form the figure,<\/p>

2<\/mn>2<\/mn><\/msup>+<\/mo>(<\/mo>y<\/mi>1<\/mn><\/msub>\u2212<\/mo>1<\/mn><\/mrow>)<\/mo><\/mrow><\/mrow>2<\/mn><\/msup>=<\/mo>y<\/mi>1<\/mn><\/msub><\/mrow>2<\/mn><\/msup><\/mrow><\/math> <\/xml><\/p>

4<\/mn>+<\/mo>y<\/mi>1<\/mn><\/msub><\/mrow>2<\/mn><\/msup>+<\/mo>1<\/mn>\u2212<\/mo>2<\/mn>y<\/mi>1<\/mn><\/msub>=<\/mo>y<\/mi>1<\/mn><\/msub><\/mrow>2<\/mn><\/msup><\/mrow><\/math> <\/xml><\/p>

5<\/mn>=<\/mo>2<\/mn>y<\/mi>1<\/mn><\/msub>\u2009<\/mtext>\u2009<\/mtext>o<\/mi>r<\/mi>\u2009<\/mtext>\u2009<\/mtext>\u2009<\/mtext>y<\/mi>1<\/mn><\/msub>=<\/mo>5<\/mn>\/<\/mo>2<\/mn><\/mrow><\/math> <\/xml><\/p>

Equation of the line form (<\/mo>2<\/mn>,<\/mo>5<\/mn>\/<\/mo>2<\/mn><\/mrow>)<\/mo><\/mrow><\/mrow><\/math> <\/xml>to the given base is<\/p>

y<\/mi>\u2212<\/mo>5<\/mn>\/<\/mo>2<\/mn>=<\/mo>2<\/mn>(<\/mo>x<\/mi>\u2212<\/mo>2<\/mn><\/mrow>)<\/mo><\/mrow><\/mrow><\/math> <\/xml>or 2<\/mn>y<\/mi>\u2212<\/mo>5<\/mn>=<\/mo>4<\/mn>(<\/mo>x<\/mi>\u2212<\/mo>2<\/mn><\/mrow>)<\/mo><\/mrow><\/mrow><\/math> <\/xml><\/p>

At y<\/mi>=<\/mo>1<\/mn><\/mrow><\/math> <\/xml>, \u2212<\/mo>3<\/mn>\/<\/mo>4<\/mn>=<\/mo>x<\/mi>\u2212<\/mo>2<\/mn><\/mrow><\/math> <\/xml><\/p>

Or x<\/mi>=<\/mo>5<\/mn>\/<\/mo>4<\/mn><\/mrow><\/math> <\/xml><\/p>

<\/p>","subject":""},"yoast_head":"\nIf the ends of the base of an isosceles triangle are at (2,0) and (0,1) and the equation of one side is x=2 \u00a0then the orthocenter of the triangle is - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"If the ends of the base of an isosceles triangle are at (2,0) and (0,1) and the equation of one side is x=2 \u00a0then the orthocenter of the triangle is\" \/>\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\/if--the-ends-of-the-base-of-an-isosceles-triangle-are-at-2\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"If the ends of the base of an isosceles triangle are at (2,0) and (0,1) and the equation of one side is x=2 \u00a0then the orthocenter of the triangle is - 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