Question

uestion 4
A is a point on the x-axis and B is (-7, 9). Distance between the points A and B
is 15 units. Find the coordinates of point A.​

Answer 1

❏ Question:-

A is a point on the x-axis and B is (-7, 9). Distance between the points A and Bis 15 units. Find the coordinates of point A.

❏ Solution:-

As, the point A is situated on the X axis so it's ordinate (y) is 0,∴ Coordinate of the point A is = (x,0)

Now, the distance between two points A(x,0) and B(-7,9) is 15 units .

$\sf\implies \sqrt{[x-(-7)]^2+[0-(9)]^2}=15$

$\sf\implies (x+7)^2+81=15^2$

$\sf\implies (x+7)^2=225-81$

$\sf\implies (x+7)^2=144$

$\sf\implies (x+7)^2=12^2$

$\sf\implies (x+7)=12$

$\sf\implies x=12-7$

$\sf\implies \boxed{\red{\large{x=5}}}$

∴ Coordinate of the point A is = (5,0)

Answer 2

Answer:

the coordinates of point A are (x,0) as it is in x-axis

now using distance formula for (x,0) and (-7,9);

____________

\| (x+7)^2+(0-9)^2 = 15 units

____________

》 \|x^2+49+14x+81. =15 units

____________

》\| ×^2+14x+130. =15

》 x^2+14x+130= 225

》 x^2+14x-95=0

x^2+19x-5x-95=0

x(x+19) -5(x+19)

(x-5)(x+19)

coordinates of x are either (5,0) or (-19,0)