Mathematics 2007 JAMB Past Questions - Question 46: Find the locus of points equidistant from two straight lines y-5=0 and y-3=0.

Correct Answer

B

Explanation

The locus of points equidistant from two straight lines in a straight line midway of the two straight lines.therefore the locud is y - 4 = 0The locus of points equidistant from two straight lines is the perpendicular bisector of the line segment connecting the two lines.The equation of the perpendicular bisector can be found by taking the midpoint of the line segment connecting the two lines and finding the negative reciprocal of the slope of that line segment.The midpoint of the line segment connecting the two lines is ((0+0)/2, (5+3)/2) = (0, 4).The slope of the line segment connecting the two lines is (3-5)/(0-0) = -2/0, which is undefined.Since the slope is undefined, the perpendicular bisector will be a vertical line passing through the midpoint (0, 4).Therefore, the locus of points equidistant from the two lines y - 5 = 0 and y - 3 = 0 is the vertical line x = 0.