A) \[y=2x+1\]
B) \[y=x+1\]
C) \[y=\frac{1}{2}x-2\]
D) \[y=x-1\]
Correct Answer: D
Solution :
Here, since ABCD is a square, A has same x-co- ordinate as that of B and same y co-ordinate as that D. \[\therefore \] \[m=-2,\text{ }n=-3\] Similarly for C, \[p=7\] and \[q=6\] To get the equation of the line that contains diagonal \[\overline{AC}\] will take the form \[y=x+c\] To get the equation of the line that contains diagonal \[\overline{AC},\] first we find the slope of AC. \[\therefore \] \[m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{2}}}=\frac{6(-3)}{7-(-2)}=\frac{6+3}{(7+2)}=\frac{9}{9}=1\] The equation of \[\overline{AC}\] will take the form \[y=mx+c\]Now, the line passed through point \[(7,6)\]. Hence to get the value of c, we substitute the values for x and y. i.e. \[6=7+c\] or \[c=6-7\] Hence equation of line \[\overline{AC}\] is, \[y=x-1\]
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