Answer
The work done is 113 meter-newtons.
Work Step by Step
Here, the object moves along the straight line, such that the angle between the force and direction of motion is ${{0}^{\circ }}$.
The object is moved from point $\left( 8,11 \right)$ to $\left( 18,20 \right)$. Therefore, the point to which the object has traveled is:
$\begin{align}
& \mathbf{AB}=\left[ \left( 18,20 \right)-\left( 8,11 \right) \right] \\
& =\left[ \left( 18-8 \right),\left( 20-11 \right) \right] \\
& =\left( 10,9 \right)
\end{align}$
$\mathbf{AB}=10\mathbf{i}+9\mathbf{j}$ …… (2)
Now, as it is known that:
$\mathbf{W}=\mathbf{F}\cdot \mathbf{AB}$ …… (3)
Substitute equation (1) and (2) in equation (3),
$\begin{align}
& \mathbf{W}=\left( 5\mathbf{i}+7\mathbf{j} \right)\left( 10\mathbf{i}+9\mathbf{j} \right) \\
& =\left[ \left( 5\times 10 \right)+\left( 7\times 9 \right) \right] \\
& =50+63 \\
& =113
\end{align}$
