Question

Find the point on the y-axis which is equal distance from the point( 5,2) and (- 4, 3)

Answer 1

Answer:

The point is (0, -2)

Step-by-step explanation:

Using the distance formula, we have:

√[(y-2)2 + (0-5)2] = √[y-3)2 + (0+4)2]

Squaring both sides and simplifying yields y2 - 4y + 29 = y2 - 6y + 25

2y = -4

  y = -2

Answer 2

General equation of amount on Y-axis is (0,y)

So let the equidistant point from points (-4,3) and (5,2) on Y-axis be(0,y)

So distance between (-4,3) and (0,y)= √[(-4-0)^2+(3-y)^2]

=√16+9-6y+y^2

=√25-6y+y^2......(1)

So distance between (5,2) and (0,y)= √[(5-0)^2+(2-y)^2]

=√25+4-4y+y^2

=√29-4y+y^2.....(2)

Since distance are equal

(1)=(2)

√25-6y+y^2=√29-4y+y^2

Cancelling square rooms on both sidesone

25-6y+y^2=29-4y+y^2

Cancelling y^2 on both sidesone

25-6y=29-4y

Re arranging similar terms

4y-6y=29-25

-2y=4

y=-2

So required point is (0,-2)