Question

4 look at triangle xyz on the graph.
which statement is true?
a all sides of the triangle have the same length.
b the length of side xy is 12.2 units.
c side yz has a length of 10.7 units.
d side xz has a length of 13 units.

Explanation:

Step1: Find coordinates of points

Assume each grid is 1 unit. Let \(X(-3,7)\), \(Y(9,5)\), \(Z(3, - 5)\)

Step2: Use distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

• For \(XY\): \(x_1=-3,y_1 = 7,x_2=9,y_2 = 5\)

\(d_{XY}=\sqrt{(9+3)^2+(5 - 7)^2}=\sqrt{144 + 4}=\sqrt{148}\approx12.166\)

• For \(YZ\): \(x_1=9,y_1 = 5,x_2=3,y_2=-5\)

\(d_{YZ}=\sqrt{(3 - 9)^2+(-5 - 5)^2}=\sqrt{36+100}=\sqrt{136}\approx11.66\)

• For \(XZ\): \(x_1=-3,y_1 = 7,x_2=3,y_2=-5\)

\(d_{XZ}=\sqrt{(3 + 3)^2+(-5 - 7)^2}=\sqrt{36+144}=\sqrt{180}\approx13.42\)

Answer:

B. The length of side \(XY\) is \(12.2\) units.