Question

6. On a coordinate plane, a right triangle with vertices at P(2, 4), ((7,9), andR(10,6). Find the lengths of the three sides to the nearest tenth.C)

Answer 1

Let us have a rough skecth of the plane as shown below

The distance between two points on a straight line is given by

`\begin{gathered} A(x_1,y_1)andB(x_2,y_2) \\ \text{distanceAB}=\sqrt[]{(y_2-y_1})^2+(x_2-x_1)^2 \end{gathered}`
`\begin{gathered} PQ=\sqrt[]{(9-4)^2+(7-2)^2} \\ =\sqrt[]{5^2_{}+5^2} \\ =\sqrt[]{25+25} \\ =\sqrt[]{50} \end{gathered}`
`\begin{gathered} PQ=\sqrt[]{50} \\ =7.071 \\ =7.1(\text{Nearest tenth)} \end{gathered}`