26. The points A ( 1 , -2 ) , B ( 2 , 3 ), C ( k , 2 )and D ( - 4 , - 3 ) are the vertices of a parallelogram. Find the value of k and the altitude of the parallelogram corresponding to the base AB.
rakhithakur:
I think minus 3 and minus 5
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let suppose that abcd is any parallelo gram
then ab= cd (opposite side of parallelogram is always equal )
by distance formula
ab square = cd square
(2-1)^2+(3+2)^3=(k+4)^2+(2+3)^2
(1)^2+(5)^2=k^2+16+8k+5^2
k^2 + 8k + 15 = 0
k^2 + 5k +3k +15 =0
k(k+5)+3(k+5)=0
(k+3)(k+5)=0
so k = -3,-5
then ab= cd (opposite side of parallelogram is always equal )
by distance formula
ab square = cd square
(2-1)^2+(3+2)^3=(k+4)^2+(2+3)^2
(1)^2+(5)^2=k^2+16+8k+5^2
k^2 + 8k + 15 = 0
k^2 + 5k +3k +15 =0
k(k+5)+3(k+5)=0
(k+3)(k+5)=0
so k = -3,-5
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