The point on the curve y = (x - 1)(x - 2) at which the tangent makes an angle of 135° with the positive direction of x-axis has coordinates

(1, 0)

Let $\left(x_1, y_1\right)$ be the required point. Then,

$\left(\frac{d y}{d x}\right)_{\left(x_1, y_1\right)}=\tan 135^{\circ}$

$\Rightarrow 2 x_1-3=-1$                 $\left[∵ y=(x-1)(x-2) \Rightarrow \frac{d y}{d x}=2 x-3\right]$

$\Rightarrow x_1=1$

Since $\left(x_1, y_1\right)$ lies on $y=(x-1)(x-2)$

∴   $y_1=\left(x_1,-1\right)\left(x_1-1\right)=(1-1)(1-2)=0$

Hence, (1, 0) is the required point.