Question

(20 points)

Point B has coordinates (5,1). The x-coordinate of point A is -3. The distance between point A and point B is 10 units. What are the possible coordinates of point A?

Answer 1

the possible coordinates are -9 and 3

Explanation:

coordinates of B=(x2,y2)= (5,1)

Coordinates of A= (x1, y1)= (-3, z)

distance= 10 units

Formula: d=
`√((y2-y1)^2+(x2-x1)^2)`

substituting the values in the above formula

10=
`√((z-(-3))^2+(-3-5)^2)`

10=
`√((z+3)^2+(-8)^2)`

10=
`√((z^2 +6z+9)+(64))`

10=
`√((z^2 +6z+73))`

taking square root on both sides

100=
`z^2 +6z+73`

100-73=
`z^2 +6z`

`z^2 +6z-27`=0

`z^2 +9z-3z-27=0`

`z(z+9) -3(z+9)=0`

`(z-3)(z+9)=0\\z-3=0 ; z+9=0\\z=3 : z=-9`