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| 1. |
Write the coordinate of a point on x-axis which is equidistant from the points (-3,4) and (7,6). |
| Answer» Let the point on the x-axis be\xa0(x,0)Distance between\xa0(x,0)\xa0and\xa0(7,6)=√(7−x)2+(6−0)2\u200b=√72+x2−14x+36 \u200b= √x2−14x+85\u200bDistance between\xa0(x,0)\xa0and\xa0(−3,4)=√(−3−x)2+(4−0)2\u200b\xa0= √32+x2+6x+16\u200b= √x2+6x+25\u200bAs the point\xa0(x,0)\xa0is equidistant from the two points, both the distancescalculated are equal.x2−14x+85\u200b=x2+6x+25\u200b=>x2−14x+85=x2+6x+2585−25=6x+14x60=20xx=3Thus, the point is\xa0(3,0) | |