Question

The distance between the points A(0,6) and B(0,–2) is

Fastest and Correct Answer will Brainiest and other correct answer will get Thank You

Result after 1 hour from now

Answer 1

Coordinate Geometry

While solving this type of question it is needed to have the knowledge of one simple formula, which is as follows:

• The formula to calculate the distance between two points.

We've been provided with two points. With this information, we've asked to calculate the distance between both points.

The given points are A(0, 6) and B(0, -2).

Then, x₁ = 0, y₁ = 6 and x₂ = 0, y₂ = -2.

Let A(x₁, y₁) and B(x₂, y₂) be two points in the coordinate plane, then the distance between A and B is given by,

$\implies\boxed{ \bf{ \: AB = \sqrt{ {(x_{1} - x_{2}) }^{2} + {(y_{2} - y_{1})}^{2} }}\:}$

By using the distance formula and substituting the known values in it, we get;

$\implies\rm{AB = \sqrt{{(0 -0)}^{2} + {( - 2 - 6)}^{2}}}$

$\implies\rm{AB = \sqrt{{(0)}^{2} + {(-8)}^{2}}}$

$\implies\rm{AB = \sqrt{0 + 64}}$

$\implies\rm{AB = \sqrt{64}}$

$\implies \boxed{\bf{AB = 8}}$

Hence, the distance between the two points is 8 units.

$\rule{90mm}{2pt}$

IMPORTANT NOTES

1. Let A(x₁, y₁) and B(x₂, y₂) be two points in the coordinate plane, then the distance between A and B is given by,

$\implies\boxed{ \rm{ \: AB = \sqrt{ {(x_{1} - x_{2}) }^{2} + {(y_{2} - y_{1})}^{2} }}\:}$

2. The distance of the point P(x, y) from the origin O(0,0) is given by,

$\implies\boxed{ \rm{ \: OP = \sqrt{x^2 + y^2}}}$

3. Any points on the x-axis is of the form (x, 0).

4. Any point on the y-axis is of the form (0, y).

Answer 2

Coordinate Geometry

Coordinate Geometry, where equations are represented by geometric curves.

We know that,

Distance between two points $\sf{A(x_1,\:x_2)\:and\:B(y_1,\:y_2)}$ is,

$AB=d={\boxed{\sqrt{(x_1\:-\:x_2)^2\:+\:(y_1\:-\:y_2)^2}}}$

We also know that, the Points of A and B are,

• $\sf{x_1\:=\:0,\:y_1\:=\:6}$
• $\sf{x_2\:=\:0,\:y_2\:=\:-2}$

Substituting values in Formula, we get,

$\implies\sf{\sqrt{(x_1\:-\:x_2)^2\:+\:(y_2\:-\:y_1)^2}}$

$\implies\sf{\sqrt{(0\:-\:0)^2\:+\:(-2\:-\:6)^2}}$

$\implies\sf{\sqrt{(0\:-\:0)^2\:+\:(2\:+\:6)^2}}$

$\implies\sf{\sqrt{(0)^2\:+\:(8)^2}}$

$\implies\sf{\sqrt{0\:+\:64}}$

$\implies\sf{\sqrt{64}}$

$\implies\sf{8}$

Hence, The Distance between A(0,6) and B(0,-2) is = 8 units.