Question

(3)
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

Solution :-

'A' is a point on X - axis and B is (-7, 9)

The general form of coordinates on X - axis are (x, 0)

So, let the the coordinates of 'A' be (x, 0)

Distance between A(x,0) and B(-7,9) = 15 units

By using Distance formula

$d = \sqrt{(x_2 - x_1)^{2} + (y_2 - y _1)^{2} }$

Here, x₁ = x, x₂ = - 7, y₁ = 0, y₂ = 9

By substituting the values

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

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

$\implies \sqrt{49 + x^{2} + 14x+ 81 } = 15$

$\implies \sqrt{x^{2} + 14x+ 130} = 15$

Squaring on both sides

⇒ x² + 14x + 130 = 15²

⇒ x² + 14x + 130 = 225

⇒ x² + 14x + 130 - 225 = 0

⇒ x² + 14x - 95 = 0

⇒ x² + 19x - 5x - 95 = 0

⇒ x(x + 19) - 5(x + 19) = 0

⇒ (x - 5)(x + 19) = 0

⇒ x - 5 = 0 or x + 19 = 0

⇒ x = 5 or x = - 19

Therefore the coordinates of A are (5,0) or (-19,0)

Answer 2

$\huge {\red{\boxed{ \overline{ \underline{ \mid\mathfrak{An}{\mathrm{sw}{ \sf{er}} \colon\mid}}}}}}$

As the point A lies on X - Axis

So, The coordinates of point A will be (x1,0)

And for B the coordinates are (-7 , 9)

And distance is 15 units.

_______________________________

Use distance Formula :

$\star {\boxed{\mathtt{Distance \: = \: \sqrt{(x_2 \: - \: x_1)^2 \: + \: (y_1 \: - \: y_2)^2}}}}$

Take,

• x1 as x
• y1 as 0
• x2 = -7
• y2 = 9

Substitute the values,

$\implies {\tt{15 \: = \: \sqrt{(-7 \: - \: x)^2 \: + \: (9 \: - \: 0)^2}}} \\ \\ \implies {\tt{15 \: = \: (-7 \: - \: x)^2 \: + \: (9)^2}} \\ \\ \implies {\tt{15 \: = \: \sqrt{(-7)^2 \: + \: (x^2) \: - \: 2(-7)(x) \: - \: 81}}} \\ \\ \implies {\tt{15 \: = \: \sqrt{49 \: + \: x^2 \: 14x \: + \: 81}}} \\ \\ \implies {\tt{15 \: = \: \sqrt{x^2 \: + \: 14x \: + \: 130}}} \\ \\ \small{\underline{\sf{\pink{\: \: \: \: \: \: \: \: \: Square \: Both \: Sides \: \: \: \: \: \: \: \:}}}} \\ \\ \implies {\tt{15^2 \: = \: x^2 \: + \: 14x \: + \: 130}} \\ \\ \implies {\tt{225 \: = \: x^2 \: + \: 14x \: + \: 130}} \\ \\ \implies {\tt{x^2 \: + \: 14x \: - \: 95 \: = \: 0}} \\ \\ \implies {\tt{x^2 \: + \: 19x \: - \: 5x \: + \: 130 \: = \: 0}} \\ \\ \implies {\tt{x(x \: + \: 19) \: - \: 5(x \: + \: 19) \: = \: 0}} \\ \\ \implies {\tt{(x\: - \: 5)(x \: + \: 19) \: = \: 0}} \\ \\ \implies {\tt{x \: - \: 5 \: 0 \: \: or \: \: x \: 19 \: = \: 0}} \\ \\ \implies {\tt{x \: = \: 5 \: \: or \: \: x \: = \: -19}}$

➠ So, The coordinates of A are (5,0) or (-19,0)