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Ram Kushwah 6 years, 11 months ago
Sorry n=6/7
And X=(--n-4)/(n+1)=(-6/7-4)/(6/7+1)
=(-6-28)/(6+7)=-34/13
So coordinates are(-34/13,0)
Ram Kushwah 6 years, 11 months ago
Soppose a point P divided the line into n:1 ratio.
The coordinates of P are
{(n×-1+1×-4)/n+1,(n×7+1×-6)/n+1}
At X axis y =0
Do 7n-6/n+1=0
7n=6. So n =7/6
Now X =(-n+4)/n+1=(-7/6+4)/(7/6+1)
(-7+24)/7+6=17/13
Do coordinates are (17/13,0)
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Honey ☺☺☺ 5 years, 8 months ago
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Sia ? 6 years, 6 months ago
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Sia ? 6 years, 6 months ago
Given: ABCD is a parallelogram whose diagonals are AC and BD.
To prove: AB2 + BC2 + CD2 + DA2 = AC2 + BD2
Construction: Draw AM {tex} \bot {/tex} DC and BN {tex} \bot {/tex} D(Produced)

Proof: In right triangle AMD and BNC.
AD = BC ..............Opp.sides of a ||gm
AM = BN ............Both are altitudes of the same parallelogram to the same base
{tex}\therefore {/tex} {tex}\triangle {/tex} AMD {tex}\cong{/tex} {tex}\triangle {/tex} BNC ................RHS congruence criterion
{tex}\therefore {/tex} MD = NC .........(1).........CPCT
In right triangle BND,
{tex}\because {/tex} {tex}\angle{/tex} N=90°
{tex}\therefore {/tex} BD2 = BN2 + DN2 .............By Pythagoras theorem
= BN2 + (DC + CN)2
= BN2 + DC2 + CN2 + 2DC.CN
= (BN2 + CN2) + CN2 + 2DC.CN
= BC2 + DC2 + 2DC.CN ..........(2)
In right triangle BNC with {tex}\angle{/tex}N = 90o
BN2+CN2 = BC2 ......By Pythagoras theorem
In right triangle AMC
{tex}\because {/tex} {tex}\angle{/tex} M=90o
{tex}\therefore {/tex} AC2 = AM2 + MC2
= AM2 = (DC - DM)2
= AM2 + DC2 + DM2 - 2DC.DM
= (AM2 + DC2) + DC2 - 2DC.DM
= AD2 + DC2 - 2DC.DM
{tex}\because {/tex} In right triangle AMD with {tex}\angle{/tex} M=90°
AD2 = AM2 + DM2 ..........[By Pythagoras theorem]
= AD2 + AB2 - DC.CN .......From(1)
Adding (3) and (2) ,we get
AC2 + BD2 = (AD2 + AB) + (BC2 + DC) = AB2 + BC2 + BC2 + CD2 + DA2
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Yogita Ingle 6 years, 11 months ago
{tex}\frac38-\;\frac1{12}\;\;=\;\frac{3(3)\;-1(2)}{24}=\;\frac{9\;-\;2}{24}=\;\frac7{24}{/tex}
Rehan Chauhan 6 years, 11 months ago
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Ashu Singh Sisodiya 6 years, 11 months ago
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