Question

Point b has coordinates (1,2). The x-coordinate of point a is -2. The distance of point a and point b is 5 units. What are the possible coordinates of point a?

Answer 1

Answer:

$(-2,6)$ and $(-2,-2)$.

Step-by-step explanation:

We have been given that point b has coordinates (1,2). The x-coordinate of point a is -2. The distance of point a and point b is 5 units.  

We will use distance formula to solve our given problem.

$D=\sqrt{(x_2-x_1)+(y_2-y_1)^2}$

Let us assume that (1,2) is $(x_1,y_1)$ and point $(-2,y)=(x_2,y_2)$

$5=\sqrt{(-2-1)^2+(y-2)^2}$

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

$5=\sqrt{9+y^2-4y+4}$

$5=\sqrt{y^2-4y+13}$

Square both sides:

$5^2=(\sqrt{y^2-4y+13})^2$

$25=y^2-4y+13$

$y^2-4y+13-25=0$

$y^2-4y-12=0$

$y^2-6y+2y-12=0$

$(y-6)(y+2)=0$

$(y-6)=0,(y+2)=0$

$(y=6,y=-2$

Therefore, the possible coordinates of point 'a' are $(-2,6)$ and $(-2,-2)$.