The distance formula:
\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
\((x_1,y_1)=(-2,4) \\
d=7 \\ \\
7=\sqrt{(x-(-2))^2+(y-4)^2} \\
7=\sqrt{(x+2)^2+(y-4)^2} \ \ \ |^2 \\
49=(x+2)^2+(y-4)^2\)
Check which point satisfies the equation:
\((x,y)=(-5,4) \\
49 \stackrel{?}{=} (-5+2)^2+(4-4)^2 \\
49 \stackrel{?}{=} (-3)^2+0^2 \\
49 \stackrel{?}{=} 9 \\
49
ot= 9 \\
doesn't \ satisfy \ the \ equation\)
\((x,y)=(-2,3) \\
49 \stackrel{?}{=} (-2+2)^2+(3-4)^2 \\
49 \stackrel{?}{=} 0^2+(-1)^2 \\
49 \stackrel{?}{=} 1 \\
49
ot= 1 \\
doesn't \ satisfy \ the \ equation\)
\((x,y)=(5,4) \\
49 \stackrel{?}{=} (5+2)^2+(4-4)^2 \\
49 \stackrel{?}{=} 7^2+0^2 \\
49 \stackrel{?}{=} 49 \\
49=49 \\
satisfies \ the \ equation\)
\((x,y)=(9,4) \\
49 \stackrel{?}{=} (9+2)^2+(4-4)^2 \\
49 \stackrel{?}{=} 11^2+0^2 \\
49 \stackrel{?}{=} 121 \\
49
ot= 121 \\
doesn't \ satisfy \ the \ equation\)
The answer is C.
