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Answered

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(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?

Sagot :

Answer:

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=[tex]\sqrt{(y2-y1)^2+(x2-x1)^2}[/tex]

substituting the values in the above formula

10=[tex]\sqrt{(z-(-3))^2+(-3-5)^2}[/tex]

10=[tex]\sqrt{(z+3)^2+(-8)^2}[/tex]

10=[tex]\sqrt{(z^2 +6z+9)+(64)}[/tex]

10=[tex]\sqrt{(z^2 +6z+73)}[/tex]

taking square root on both sides

100=[tex]z^2 +6z+73[/tex]

100-73=[tex]z^2 +6z[/tex]

[tex]z^2 +6z-27[/tex]=0

[tex]z^2 +9z-3z-27=0[/tex]

[tex]z(z+9) -3(z+9)=0[/tex]

[tex](z-3)(z+9)=0\\z-3=0 ; z+9=0\\z=3 : z=-9[/tex]

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