{"id":652432,"date":"2023-06-27T08:52:56","date_gmt":"2023-06-27T03:22:56","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/the-area-of-the-triangle-formed-by-the-line-xayb1-with-the-coordinate-axes-is\/"},"modified":"2025-06-26T15:37:58","modified_gmt":"2025-06-26T10:07:58","slug":"the-area-of-the-triangle-formed-by-the-line-xayb1-with-the-coordinate-axes-is","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/the-area-of-the-triangle-formed-by-the-line-xayb1-with-the\/","title":{"rendered":"The area of the triangle formed by the line xa+yb=1 with the coordinate axes is:"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"The area of the triangle formed by the line xa+yb=1 with the coordinate axes is:","custom_permalink":"question\/mathematics\/the-area-of-the-triangle-formed-by-the-line-xayb1-with-the\/"},"categories":[],"acf":{"question":"

The area of the triangle formed by the line <\/span>x<\/mi><\/mrow>a<\/mi><\/mrow><\/mfrac>+<\/mo>y<\/mi><\/mrow>b<\/mi><\/mrow><\/mfrac>=<\/mo>1<\/mn><\/math> with the coordinate axes is:<\/span><\/p>

<\/p>

<\/p><\/spanstyle=\"-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:0pt\"><\/spanstyle=\"-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:0pt\">","options":[{"option":"ab<\/mi><\/math>","correct":false},{"option":"2<\/mn>ab<\/mi><\/math>","correct":false},{"option":"1<\/mn><\/mrow>2<\/mn><\/mrow><\/mfrac>ab<\/mi><\/math>","correct":true},{"option":"1<\/mn><\/mrow>4<\/mn><\/mrow><\/mfrac>ab<\/mi><\/math> <\/span>","correct":false}],"solution":"We have been given the lines <\/span>x<\/mi>=<\/mo>0<\/mn><\/math>, <\/span>y<\/mi>=<\/mo>0<\/mn><\/math> and <\/span>x<\/mi><\/mrow>a<\/mi><\/mrow><\/mfrac>+<\/mo>y<\/mi><\/mrow>b<\/mi><\/mrow><\/mfrac>=<\/mo>1<\/mn><\/math>.<\/span>
We need to find the area of the triangle formed by the line <\/span>x<\/mi><\/mrow>a<\/mi><\/mrow><\/mfrac>+<\/mo>y<\/mi><\/mrow>b<\/mi><\/mrow><\/mfrac>=<\/mo>1<\/mn><\/math> with the coordinate axes.<\/span>
Substitute 0 for y in <\/span>x<\/mi><\/mrow>a<\/mi><\/mrow><\/mfrac>+<\/mo>y<\/mi><\/mrow>b<\/mi><\/mrow><\/mfrac>=<\/mo>1<\/mn><\/math> to find the x intercept of the line.<\/span>
x<\/mi><\/mrow>a<\/mi><\/mrow><\/mfrac>+<\/mo>0<\/mn><\/mrow>b<\/mi><\/mrow><\/mfrac>=<\/mo>1<\/mn><\/math>
\u21d2<\/mo>x<\/mi><\/mrow>a<\/mi><\/mrow><\/mfrac>+<\/mo>0<\/mn>=<\/mo>1<\/mn><\/math>
\u21d2<\/mo>x<\/mi><\/mrow>a<\/mi><\/mrow><\/mfrac>=<\/mo>1<\/mn><\/math>
\u21d2<\/mo>x<\/mi>=<\/mo>a<\/mi><\/math>
Substitute 0 for x in <\/span>x<\/mi><\/mrow>a<\/mi><\/mrow><\/mfrac>+<\/mo>y<\/mi><\/mrow>b<\/mi><\/mrow><\/mfrac>=<\/mo>1<\/mn><\/math> to find the y intercept of the line.<\/span>
x<\/mi><\/mrow>a<\/mi><\/mrow><\/mfrac>+<\/mo>y<\/mi><\/mrow>b<\/mi><\/mrow><\/mfrac>=<\/mo>1<\/mn><\/math>
\u21d2<\/mo>0<\/mn><\/mrow>a<\/mi><\/mrow><\/mfrac>+<\/mo>y<\/mi><\/mrow>b<\/mi><\/mrow><\/mfrac>=<\/mo>1<\/mn><\/math>
\u21d2<\/mo>0<\/mn>+<\/mo>y<\/mi><\/mrow>b<\/mi><\/mrow><\/mfrac>=<\/mo>1<\/mn><\/math>
\u21d2<\/mo>y<\/mi><\/mrow>b<\/mi><\/mrow><\/mfrac>=<\/mo>1<\/mn><\/math>
\u21d2<\/mo>y<\/mi>=<\/mo>b<\/mi><\/math>
Thus, we have three coordinates, (0,0), (a, 0), (0, b).<\/span>
On plotting the points on a graph, we get,<\/span>
\"\"Now, the area of the triangle formed by the line <\/span>x<\/mi><\/mrow>a<\/mi><\/mrow><\/mfrac>+<\/mo>y<\/mi><\/mrow>b<\/mi><\/mrow><\/mfrac>=<\/mo>1<\/mn><\/math> with the coordinate axes is equal to the area of triangle ABC.<\/span>
The formula of the area of a triangle is,<\/span>
A<\/mi>=<\/mo>1<\/mn><\/mrow>2<\/mn><\/mrow><\/mfrac>\u00d7<\/mo>base<\/mi>\u00d7<\/mo>height<\/mi><\/math>
\u21d2<\/mo>A<\/mi>=<\/mo>1<\/mn><\/mrow>2<\/mn><\/mrow><\/mfrac>\u00d7<\/mo>AB<\/mi>\u00d7<\/mo>AC<\/mi><\/math>
\u21d2<\/mo>A<\/mi>=<\/mo>1<\/mn><\/mrow>2<\/mn><\/mrow><\/mfrac>\u00d7<\/mo>a<\/mi>\u00d7<\/mo>b<\/mi><\/math>
Hence, the area of triangle is <\/span>A<\/mi>=<\/mo>1<\/mn><\/mrow>2<\/mn><\/mrow><\/mfrac>ab<\/mi><\/math>.<\/span>
Hence, option 3 is correct.<\/span>
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