Math, asked by soubhyagya, 1 month ago

find the distance between the following pair of point(-3,0),(-1,-2)​

Answers

Answered by anindyaadhikari13
22

\texttt{\textsf{\large{\underline{Answer}:}}}

  • The distance between the two points (-3, 0) and (-1, -2) is – unit.

\texttt{\textsf{\large{\underline{Solution}:}}}

Given Points: (-3, 0) and (-1, -2)

Distance between two points is calculated by using the formula given below:

 \sf \implies D =  \sqrt{ {(x}_{2} -  x_{1})^{2} + {(y}_{2} -  y_{1})^{2} }

Here:

 \sf \implies \begin{cases} \sf x_{1} =  - 3 \\ \sf x_{2}  =  - 1 \\ \sf y_{1} = 0 \\ \sf y_{2} =  - 2\end{cases}

Substitute the value in the formula, we get:

 \sf \implies D =  \sqrt{ ( - 1 + 3)^{2} + ( - 2)^{2} }

 \sf \implies D =  \sqrt{4 + 4 }

 \sf \implies D =  \sqrt{8}

 \sf \implies D =  \sqrt{4 \times 2}

 \sf \implies D =  \sqrt{4}  \times  \sqrt{2}

 \sf \implies D =  2 \sqrt{2}

So, the distance between the two points is 2√2 unit.

\texttt{\textsf{\large{\underline{Learn More}:}}}

1. Section formula.

Let P(x₁, y₁) and Q(x₂, y₂) be two points in the coordinate plane and R(x, y) be the point which divides PQ internally in the ratio m₁ : m₂. Then, the coordinates of R will be:

\sf\implies R = \bigg(\dfrac{m_{1}x_{2}+m_{2}x_{1}}{m_{1}+m_{2}}, \dfrac{m_{1}y_{2}+m_{2}y_{1}}{m_{1}+m_{2}}\bigg)

2. Mid-point formula.

Let P(x₁, y₁) and Q(x₂, y₂) be two points in the coordinate plane and R(x, y) be the mid-point of PQ. Then, the coordinates of R will be:

\sf\implies R = \bigg(\dfrac{x_{1}+x_{2}}{2}, \dfrac{y_{1}+y_{2}}{2}\bigg)

3. Centroid of a triangle.

Centroid of a triangle is the point where the medians of the triangle meet.

Let A(x₁, y₁), B(x₂, y₂) and C(x₃, y₃) be the vertices of a triangle. Let R(x, y) be the centroid of the triangle. Then, the coordinates of R will be:

\sf\implies R = \bigg(\dfrac{x_{1}+x_{2}+x_{3}}{3}, \dfrac{y_{1}+y_{2}+y_{3}}{3}\bigg)


anindyaadhikari13: Thanks for the brainliest :)
Answered by kamalrajatjoshi94
1

Answer:

Using distance formula:-

 \sqrt{ {(x2 - x1)}^{2} + ( {y2 - y1)}^{2}  }

 =  \sqrt{( { - 3 -</p><p>+ 1)}^{2} +  {(0 - 2)}^{2}   }

 =    \sqrt{ { - 2}^{2}  +  { - 2}^{2}  }

 =  \sqrt{4 + 4}

 =  \sqrt{8}

 = \sqrt{ {2}^{2}  }

 = 2 \sqrt{2}

=2×1.414

=2.828

Similar questions