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MAXImum [283]
3 years ago
9

t%20%5Clarge%20Distance%20%20%5C%3A%20Formula%20%5C%3A%20%20%20%5C%5C%20%20%5Clarge%20%5Ctt%20and%20%5C%5C%20%5Clarge%5Ctt%20%20%5C%3A%20Coordinate%20%20%5C%3A%20Proof%20%5Cend%7Barray%7D%7D%7D" id="TexFormula1" title=" \boxed{\boxed{ \begin{array}{}\large\tt The \\ \tt \large Distance \: Formula \: \\ \large \tt and \\ \large\tt \: Coordinate \: Proof \end{array}}}" alt=" \boxed{\boxed{ \begin{array}{}\large\tt The \\ \tt \large Distance \: Formula \: \\ \large \tt and \\ \large\tt \: Coordinate \: Proof \end{array}}}" align="absmiddle" class="latex-formula">
Direction: Find the distance between each pair of points on the coordinate plane and write the solution.


1. A(3, 8) and B(3, -2)

2. O(5, -2) and K(7, -2)

3. L(4, -4) and M(-4, 6)

4. P(5, 1) and C(2, 3)

5. Q(-10, 9) and R(-2, 3)

\boxed{\boxed{ \begin{array}{}\large\tt Nonsense + Useless \\   \large \tt= Report! \end{array}}}
​
Mathematics
2 answers:
larisa86 [58]3 years ago
8 0

Distance formula

\boxed{\sf \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}

Now

#1

\\ \tt\Rrightarrow AB=\sqrt{(3-3)^2+(-2-8)^2}=\sqrt{100}=10units

#2

\\ \tt\Rrightarrow OK=\sqrt{(5-7)^2+(-2+2)^2}=\sqrt{4}=2units

#3

\\ \tt\Rrightarrow LM=\sqrt{(-4-4)^2+(6+4)^2}=\sqrt{64+100}=\sqrt{164}\approx 13units

#4

\\ \tt\Rrightarrow PC=\sqrt{(5-2)^2+(1-3)^2}=\sqrt{9+4}=\sqrt{13}=3.2units

#5

\\ \tt\Rrightarrow QR=\sqrt{(-2+10)^2+(3-9)^2}=\sqrt{64+36}=\sqrt{100}=10units

RUDIKE [14]3 years ago
7 0

Answer:

Answer of all given questions are given below :

  • 1) AB = 10 units
  • 2) OK = 2 units
  • 3) LM = 2√41 units
  • 4) PC ≈ 3.6 units
  • 5) QR = 10 units

Step-by-step explanation:

Here's the required formula to find distance between points :

\star{\small{\underline{\boxed{\sf{\red{Distance = \sqrt{\Big(x_{2} - x_{1} \Big)^{2} + \Big(y_{2} - y_{1} \Big)^{2}}}}}}}}

According to this formula, we'll solve all the given questions and find the distance between points.

1. A(3, 8) and B(3, -2)

Substituting all the given values in the formula to find the distance between points:

{\implies{\small{\sf{Distance = \sqrt{\Big(x_{2} - x_{1} \Big)^{2} + \Big(y_{2} - y_{1} \Big)^{2}}}}}}

{\implies{\small{\sf{AB = \sqrt{\Big(3 - 3 \Big)^{2} + \Big( - 2 - 8 \Big)^{2}}}}}}

{\implies{\small{\sf{AB = \sqrt{\Big(0\Big)^{2} + \Big(  - 10 \Big)^{2}}}}}}

{\implies{\small{\sf{AB = \sqrt{\Big(0 \times 0\Big) + \Big(  - 10 \times  - 10 \Big)}}}}}

{\implies{\small{\sf{AB = \sqrt{\big(0 + 100\big)}}}}}

{\implies{\small{\sf{AB = \sqrt{100}}}}}

{\implies{\sf{\underline{\underline{\purple{AB = 10}}}}}}

Hence, the distance between points AB is 10 units..

\begin{gathered}\end{gathered}

2. O(5, -2) and K(7, -2)

Substituting all the given values in the formula to find the distance between points:

{\longrightarrow{\small{\sf{Distance = \sqrt{\Big(x_{2} - x_{1} \Big)^{2} + \Big(y_{2} - y_{1} \Big)^{2}}}}}}

{\longrightarrow{\small{\sf{OK = \sqrt{\Big(7 - 5\Big)^{2} + \Big( - 2  + 2 \Big)^{2}}}}}}

{\longrightarrow{\small{\sf{OK = \sqrt{\Big(2\Big)^{2} + \Big(0 \Big)^{2}}}}}}

{\longrightarrow{\small{\sf{OK = \sqrt{\Big(2 \times 2\Big) + \Big(0 \times 0 \Big)}}}}}

{\longrightarrow{\small{\sf{OK = \sqrt{\big(4 + 0 \big)}}}}}

{\longrightarrow{\small{\sf{OK = \sqrt{4}}}}}

{\longrightarrow{\sf{\underline{\underline{\pink{OK = 2}}}}}}

Hence, the distance between points OK is 2 units.

\begin{gathered}\end{gathered}

3. L(4, -4) and M(-4, 6)

Substituting all the given values in the formula to find the distance between points:

{\longmapsto{\small{\sf{Distance = \sqrt{\Big(x_{2} - x_{1} \Big)^{2} + \Big(y_{2} - y_{1} \Big)^{2}}}}}}

{\longmapsto{\small{\sf{LM = \sqrt{\Big( - 4 - 4\Big)^{2}  +  \Big( 6 + 4 \Big)^{2}}}}}}

{\longmapsto{\small{\sf{LM = \sqrt{\Big( - 8\Big)^{2}  +  \Big(10 \Big)^{2}}}}}}

{\longmapsto{\small{\sf{LM = \sqrt{\Big( - 8 \times  - 8\Big) +  \Big(10  \times 10\Big)}}}}}

{\longmapsto{\small{\sf{LM = \sqrt{\big( 64 + 100\big)}}}}}

{\longmapsto{\small{\sf{LM = \sqrt{164}}}}}

{\longmapsto{\sf{\underline{\underline{\orange{LM = 2 \sqrt{41} }}}}}}

Hence, the distance between points LM is 2√41 units.

\begin{gathered}\end{gathered}

4. P(5, 1) and C(2, 3)

Substituting all the given values in the formula to find the distance between points:

{\dashrightarrow{\small{\sf{Distance = \sqrt{\Big(x_{2} - x_{1} \Big)^{2} + \Big(y_{2} - y_{1} \Big)^{2}}}}}}

{\dashrightarrow{\small{\sf{PC = \sqrt{\Big(2 - 5 \Big)^{2} + \Big(3  - 1 \Big)^{2}}}}}}

{\dashrightarrow{\small{\sf{PC = \sqrt{\Big( - 3\Big)^{2} + \Big(2\Big)^{2}}}}}}

{\dashrightarrow{\small{\sf{PC = \sqrt{\Big( - 3 \times  - 3\Big) + \Big(2 \times 2\Big)}}}}}

{\dashrightarrow{\small{\sf{PC = \sqrt{\big( 9 + 4\big)}}}}}

{\dashrightarrow{\small{\sf{PC = \sqrt{13}}}}}

{\dashrightarrow{\sf{\underline{\underline{\green{PC \approx 3.6}}}}}}

Hence, the distance between points PC is 3.6 units.

\begin{gathered}\end{gathered}

5. Q(-10, 9) and R(-2, 3)

Substituting all the given values in the formula to find the distance between points:

{\twoheadrightarrow{\small{\sf{Distance = \sqrt{\Big(x_{2} - x_{1} \Big)^{2} + \Big(y_{2} - y_{1} \Big)^{2}}}}}}

{\twoheadrightarrow{\small{\sf{QR = \sqrt{\Big( - 2 + 10 \Big)^{2} + \Big(3 - 9 \Big)^{2}}}}}}

{\twoheadrightarrow{\small{\sf{QR = \sqrt{\Big( 8 \Big)^{2} + \Big( - 6\Big)^{2}}}}}}

{\twoheadrightarrow{\small{\sf{QR = \sqrt{\Big( 8 \times 8 \Big)+ \Big( - 6 \times  - 6\Big)}}}}}

{\twoheadrightarrow{\small{\sf{QR = \sqrt{\big(64  + 36\big)}}}}}

{\twoheadrightarrow{\small{\sf{QR = \sqrt{100}}}}}

{\twoheadrightarrow{\sf{\underline{\underline{\blue{QR = 10}}}}}}

Hence, the distance between points QR is 10 units.

\rule{300}{2.5}

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