Math, asked by nehahirve25, 6 months ago

The mid point of the line segment joining A(2,p) and
B(q,4) is(3,5).calculate the value of p and q.​

Answers

Answered by Anonymous
37

\huge\underline{\bf{Given}}

⠀|━━━━━━━━━━━|━━━━━━━━━━━|

A(2,p)⠀⠀⠀⠀⠀⠀⠀P(3,5)⠀⠀⠀⠀⠀⠀⠀⠀B(q,4)

  • AB is a line segment with points A(2,p) and B(q,4).
  • Point P(3,5) is the mid point of the line segment AB.

\huge\underline{\bf{To\: find}}

  • Value of p and q.

\huge\underline{\bf{Concept}}

  • Mid - point formula.

\huge\underline{\bf{Solution}}

  • We have two points of line segment AB, and it is also given that P is the mid point of the line segment.
  • Now, we need to find out the value of p and q.

⠀⠀❍ ᴜsɪɴɢ ᴍɪᴅ - ᴘᴏɪɴᴛ ғᴏʀᴍᴜʟᴀ

\: \: \: \: \: \boxed{\bf{\orange{P(x,y) = \bigg( \dfrac{x_1 + x_2}{2} , \dfrac{y_1 + y_2}{2} \bigg)}}}

Here,

  • \sf{x_1 = 2, x_2 = q}
  • \sf{y_1 = p, y_2 = 4}

\tt:\implies{P(3,5) = \bigg\lgroup{\dfrac{2 + q}{2}}, \dfrac{p + 4}{2}\bigg\rgroup}

⠀⠀❍ ᴏɴ ᴄᴏᴍᴘᴀʀɪɴɢ

\bf\longmapsto\: \: \: \: \: \: \: \: \:{\dfrac{2 + q}{2} = 3}

\tt\longmapsto\: \: \: \: \: \: \: \: \:{2 + q = 6}

\tt\longmapsto\: \: \: \: \: \: \: \: \:{q = 6 - 2}

\tt\longmapsto\: \: \: \: \: \: \: \: \:{\boxed{\red{q = 4}}}

⠀⠀❍ sɪᴍɪʟᴀʀʟʏ

\bf\longmapsto\: \: \: \: \: \: \: \: \:{\dfrac{p + 4}{2} = 5}

\tt\longmapsto\: \: \: \: \: \: \: \: \:{p + 4 = 10}

\tt\longmapsto\: \: \: \: \: \: \: \: \:{p = 10 - 4}

\tt\longmapsto\: \: \: \: \: \: \: \: \:{\boxed{\red{p = 6}}}

Hence,

  • Value of p = 6
  • Value of q = 4

━━━━━━━━━━━━━━━━━━━━━━

Answered by Anonymous
92

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

\large{\underline{\sf{\red{Required\:Answer:}}}}

  • \large\boxed{\underline{{\sf Value\:of\:p=6  }}}

  • \large\boxed{\underline{{\sf Value\:of\:q=4  }}}

Given:-

  • \sf{A = (2,p) = (x_1,y_1)}

  • \sf{B = (q,4) = (x_2,y_2)}

  • \sf{C = (3,5) = (x,y)}

To Find:-

  • Value of p and q.

Solution:-

By mid-term formula:-

\large\boxed{\underline{{\sf x=\dfrac{(x_1+x_2)}{2} ,\dfrac{(y_1+y_2)}{2}  }}}

:\implies\:\: \sf{3=\dfrac{(2+q)}{2}}

:\implies\:\: \sf{\dfrac{(2+q)}{2}=3}

:\implies\:\: \sf{\dfrac{2(2+q)}{2}=3 \times 2}

:\implies\:\: \sf{2+q=6}

:\implies\:\: \sf{2+q-2=6-2}

\sf:\implies \underline{\boxed{\pink{\mathfrak{q=4}}}}\:\:\bigstar

And,

:\implies\:\: \sf{5=\dfrac{(p+4)}{2}}

:\implies\:\: \sf{\dfrac{(p+4)}{2}=5}

:\implies\:\: \sf{\dfrac{2(p+4)}{2}=5 \times 2}

:\implies\:\: \sf{p+4=10}

\sf{:\implies\:\: \sf{p=10-4}}

\sf:\implies \underline{\boxed{\pink{\mathfrak{p=6}}}}\:\:\bigstar

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Similar questions