Question

The coordinates of the point on the curve $y=x^2-3x+2$, where the tangent is perpendicular to the straight line $y=x$ are

• A. $(0,2)$
• B. $(1,0)$
• C. $(-1,6)$
• D. $(2,-2)$

Answer 1

The correct option is B

$(1,0)$

Explanation for the correct option:

Finding the coordinates of the point:

The given line is $y=x$

Then slope $m_1=1$

Consider the slope of the tangent line to be $m_2$

As given the tangent to the curve is perpendicular to the straight line $y=x$, then,

$$\begin{gathered} \Rightarrow m_1{m}_2=-1 \\ \Rightarrow \left(1\right)m_2=-1 \\ \Rightarrow m_2=-1 \end{gathered}$$

The given curve is $y=x^2-3x+2...\left(i\right)$

Differentiating it w.r.t. $x$

$$\begin{gathered} \Rightarrow \frac{dy}{dx}=m_2=2x–3 \\ \Rightarrow -1=2x–3 \\ \Rightarrow 2=2x \\ \Rightarrow x=1 \\ \text{Substituting the value of}x\text{in the equation}y=x^2-3x+2 \\ \therefore y=1–3+2 \\ \Rightarrow y=0 \end{gathered}$$

Thus, the point is $(1,0)$

Hence, option (B) is correct.