Question

Find the point on x-axis which is equidistant from the points (2,-2) and (-4,2)​

Answer 1

Answer: (-1, 0)

Let the point which is equidistant from the two given points A(2, -2) and B(-4, 2) be C(x, 0)

The ordinate of the point C is taken as 0 because it is on the x-axis as given in the question.

Which means,

⇒ AC = BC

Using the distance formula which gives the distance between two points (x₁, y₁) and (x₂, y₂) as,

• √{ (x₂ - x₁)² + (y₂ - y₁)² }

Now, Substituting the required values, we get

⇒ √{ (x - 2)² + (y + 2)² } = √{ (x + 4)² + (y - 2)²

Squaring the both sides,

⇒ (x - 2)² + (0 + 2)² = (x + 4)² + (0 - 2)²

⇒ x² + 4 - 4x + 4 = x² + 16 + 8x + 4

⇒ 8 - 4x = 20 + 8x

⇒ 8x + 4x = 8 - 20

⇒ 12x = -12

⇒ x = -1

Hence, The required point is (-1, 0).

Some Information:-

• The coordinate of the midpoint of a line segment between the points (x₁, y₁) and (x₂, y₂) is given as

x-coordinate = (x₁ + x₂) / 2

y-coordinate = (y₁ + y₂) / 2

Answer 2

___________________

Let Р (x,0) be а роint оn x-аxis

PA = PB

PA² = PB²

• (x-2)² + (0+2)² = (x+4)² + (0-2)²
• x² + 4 - 4x + 4
• x²+16 + 8x+4
• -4x + 4 = 8x+16
• x = -1

P (-1,0)

___________________

hope it helps