Answer :
To find the locus of points where the abscissa (x) and ordinate (y) are equal, we start by defining the relationship between these two coordinates. If the abscissa and ordinate are equal, it means that:
[tex]\[ x = y \][/tex]
This can be rearranged to form an equation that describes this relationship:
[tex]\[ x - y = 0 \][/tex]
Thus, the equation representing the locus of points where the abscissa equals the ordinate is:
[tex]\[ x - y = 0 \][/tex]
Now we compare this with the given options:
a) [tex]\( x + y + 1 = 0 \)[/tex]
b) [tex]\( x - y = 0 \)[/tex]
c) [tex]\( x + y = 1 \)[/tex]
d) None of these
The correct choice is:
b) [tex]\( x - y = 0 \)[/tex]
So, the answer is:
b) [tex]\( x - y = 0 \)[/tex]
[tex]\[ x = y \][/tex]
This can be rearranged to form an equation that describes this relationship:
[tex]\[ x - y = 0 \][/tex]
Thus, the equation representing the locus of points where the abscissa equals the ordinate is:
[tex]\[ x - y = 0 \][/tex]
Now we compare this with the given options:
a) [tex]\( x + y + 1 = 0 \)[/tex]
b) [tex]\( x - y = 0 \)[/tex]
c) [tex]\( x + y = 1 \)[/tex]
d) None of these
The correct choice is:
b) [tex]\( x - y = 0 \)[/tex]
So, the answer is:
b) [tex]\( x - y = 0 \)[/tex]
