Question

Find all points having an x-coordinate of 5 whose distance from the point (2, 6) is 5

Answer 1

The points are (5,2) and (5,10)

Explanation:

we know that

the formula to calculate the distance between two points is equal to

`d=\sqrt{(y2-y1)^(2)+(x2-x1)^(2)}`

we have

`(2,6)\ and\ (5,y)\\d=5\ units`

substitute in the formula

`5=\sqrt{(y-6)^(2)+(5-2)^(2)}`

solve for y

`5=\sqrt{(y-6)^(2)+(3)^(2)}`

`5=\sqrt{(y-6)^(2)+9`

squared both sides

`25=(y-6)^(2)+9`

`(y-6)^(2)=25-9`

`(y-6)^(2)=16`

square root both sides

`(y-6)=\pm4`

`y=6\pm4`

so

`y=6+4=10`

`y=6-4=2`

therefore

The points are (5,2) and (5,10)