Question

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

Answer 1

Answer:

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

Step-by-step 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)