Find the equation of the locus of the points that are equidistant from points (-1,0) and (1,0)
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The locus is the perpendicular bisector of the line segment joining the two points. In this case, the y-axis!
To find the equation of the locus of points that are equidistant from two given points, you can use the concept of the perpendicular bisector.
First, find the midpoint between the two given points, (-1,0) and (1,0). The midpoint formula is given by:
Midpoint (x₀, y₀) = ((x₁ + x₂)/2 , (y₁ + y₂)/2)
In this case, the midpoint is (0,0).
Next, find the slope of the line connecting the two given points. The slope formula is given by:
Slope m = (y₂ - y₁) / (x₂ - x₁)
In this case, since both points have a y-coordinate of 0, the slope is undefined or infinite.
Now, we know that the perpendicular bisector of a line segment is the line that intersects the midpoint of the line segment at a right angle. Since the slope of the line connecting the two given points is undefined, the slope of the perpendicular bisector is 0.
Using point-slope form, where y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope, we can substitute the values we know:
y - 0 = 0(x - 0)
y = 0
So, the locus of points that are equidistant from (-1,0) and (1,0) is the line y = 0, which is the x-axis.
Therefore, the equation of the locus of the points is y = 0.