Question

The points $(1,7)$, $(4,2)$, $(-1,-1)$ and $(-4,4)$ are the vertices of a:

• A. parallelogram
• B. rhombus
• C. rectangle
• D. square

Answer 1

Answer: (D)

square

Let $A(1,7),B(4,2),C(-1,-1)$ and $D(4,4)$
Distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ can be calculated using the formula $\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$
Distance between the points A$(1,7)$ and B $(4,2)=\sqrt{{(4-1)}^2+{(2-7)}^2}=\sqrt{9+25}=\sqrt{34}$

Distance between the points B$(4,2)$ and C $(-1,-1)=\sqrt{{(-1-4)}^2+{(-1-2)}^2}=\sqrt{25+9}=\sqrt{34}$

Distance between the points C$(-1,-1)$ and D $(-4,4)=\sqrt{{(-4+1)}^2+{(4+1)}^2}=\sqrt{9+25}=\sqrt{34}$

Distance between the points A$(1,7)$ and D $(-4,4)=\sqrt{{(-4-1)}^2+{(4-7)}^2}=\sqrt{25+9}=\sqrt{34}$

Since, length of the sides between all vertices are equal, they are the vertices of a square.