A point P(x,y) moves such that it is equidistant from the points (-4,7) and (3,-2). What is the equation that represent this locus?
I don't know how to do this question. Please help.
Thanks.
Hello, shenton,
the point P moves on the perpendicular bisector of the straight line from A(-4, 7) and B(3, -2).
1. Calculate the coordinates of the midpoint M of AB: M((-4+3)/2, (7-2)/2)
2. Calculate the slope of AB: (7-(-2))/(-4-3) = -9/7
3. The perpendicular direction is therefore: m = 7/9
Now you have a point and the slope of the line you are looking for. Use the point-slope-formula of a line:
(y - 5/2)/(x - (-1/2)) = 7/9 . Multiply by the denominator:
y - 5/2 = 7/9x + 7/18 Finally you get:
y = 7/9x + 26/9
EB
Hello, shenton!
Hey, how about using the Distance Formula?A point P(x,y) moves such that it is equidistant from the points A(-4,7) and B(3,-2).
What is the equation that represent this locus?
. . . . . . . - . - . . . . . ._______________
The distance PA is: . √(x + 4)² + (y - 7)²
. . . . . . . - . - . . . . . ._______________
The distance PB is: . √(x - 3)² + (y + 2)²
. . . . . . . . . . . . . _______________ . . - . ._______________
Since PA = PB: . √(x + 4)² + (y - 7)² . = . √(x - 3)² + (y + 2)²
Square both sides: . (x + 4)² + (y - 7)² . = . (x - 3)² + (y + 2)²
Expand: . x² + 8x + 16 + y² - 14y + 49 . = . x² - 6x + 9 + y² + 4y + 4
. . which simplifies to: . 14x - 18y + 52 .= .0 . → . y .= .(7/9)x + 26/9