Find the point (x, y) on the line y=x that is equidistant from the points (−1, −5) and (−1, −3)

Question

precalculus

Answer 1

wanna tri find a point on a line y=x  & same distans from 2 points

(-1, -3) & (-1, -5)

Aent no such point

distans=shortest distans=on perpendikular tu start line

point (-1,-3): distans=1.4142135, & point on line is (-2,-2)

point (-1,-5): distans=2.82842712, & point on line is (-3,-3)

Answer 2

assume theer is such a point (x0, y0)

then 2 lines the same lengths go from it tu (-1,-3) & (-1,-5)

join thees 2 points & yu hav isosolees triangel

draw perpendikular bisekter av base & it go thru top av iso triangel=spot on line

2 base points vertikal, so bisekter is horizontal,

thus spot on line is at y=-4  (weer bisekter kut base av triangel)

Thus, spot on line is(-4,-4)