Mathematics: (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?

I m currently taking 10th grade geometry, so I can help you with as much as I can....

(20 points) Point B has coordinates (5,1). The

lyssa128

09.03.2022

the possible coordinates are -9 and 3

Step-by-step explanation:

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

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

distance= 10 units

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

substituting the values in the above formula

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

10= $\sqrt{(z+3)^2+(-8)^2}$

10= $\sqrt{(z^2 +6z+9)+(64)}$

10= $\sqrt{(z^2 +6z+73)}$

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

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

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