ANSWER
Point D
EXPLANATION
The distance between two points (x₁, y₁) and (x₂, y₂) is given by the Pythagorean Theorem,
[tex]d=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]
Let's find the distance between points A and B,
[tex]d_{AB}=\sqrt[]{(1-4)^2+(1-4)^2}=\sqrt[]{(-3)^2+(-3)^2}=\sqrt[]{9+9}=\sqrt[]{18}\approx4.2[/tex]
The distance between points A and C is,
[tex]d_{AC}=\sqrt[]{(1-(-3))^2+(1-4)^2}=\sqrt[]{(4)^2+(-3)^2}=\sqrt[]{16+9}=\sqrt[]{25}=5[/tex]
And the distance between points A and D is,
[tex]d_{AD}=\sqrt[]{(1-(-4)^2+(1-(-4)^2}=\sqrt[]{(1+4)^2+(1+4)^2}=\sqrt[]{(5)^2+(5)^2}=\sqrt[]{25+25}=\sqrt[]{50}\approx7.1[/tex]
Hence, point D is at approximately 7.1 units from point A.
