Question

Which of these is the relation between x and y if (x, y) is equidistant from (-2, 1) and (7, 4)?

1 )3x + y = 10

2) 5x + 3y = 30

3 )x + 3y = 18

4) y - x = 6

Answer 1

Answer:

Answer

Let P(x,y) be equidistant from the points A(7,1) and B(3,5).

AP=BP

AP

2

=BP

2

(x−7)

2

+(y−1)

2

=(x−3)

2

+(y−5)

2

x

2

−14x+49+y

2

−2y+1=x

2

−6x+9+y

2

−10y+25

x−y=2

Answer

Consider the equations:

3x−4y=25...(1)

−2x+y=−10...(2)

Multiply equation (2) by 4, we get

−2x(4)+y(4)=−10(4)

⇒ −8x+4y=−40...(3)

Now add equation (1) and (3), we get

3x−8x−4y+4y=25−40

⇒−5x=−15

⇒x=3

Substitute x=3 in equation (2)

−2(3)+y=−10

⇒−6+y=−10

⇒−y=−10+6

⇒−y=−4

Hence, x=3 and y=−4