Question

On a set of steps, the first step from the base of the steps is labeled 111, the second is labeled 2, and so on. Each step has the same height. The table below shows the step number and step's height from the base of the steps.
Step number Height from the base (meters)
50 10
90 18
110 2

Answer 1

Answer:

\large\qquad \qquad \underline{ \pmb {{ \mathbb{ \maltese \: ANSWER :-) \: \: \text3 }}}}✠ANSWER:−)3✠ANSWER:−)3

\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: SOLUTION}}}}}✠SOLUTION✠SOLUTION

Given points (1,2) , (3,4) and (h,k) are on Line L1,

\begin{gathered} \underline\mathcal{ \bigstar So, \: Slope \: \: of \: \: Line \: \: L_1 \: \: is } \\ \\ m_1= \dfrac{4-2}{-3-1} = \sf { { }{} \frac{k - 2}{h - 1} } \\ \\ \implies \bf m_1 = \bf \frac{ - 1}{2 } = \bf\frac{ h- 2}{k - 1} \\ \\ \implies2(k - 2) = - 1(h - 1) \\ \\ \implies \boxed{ \boxed{ \bf h + 2k = 5}}...(i)\end{gathered}★So,SlopeofLineL1ism1=−3−14−2=h−1k−2⟹m1=2−1=k−1h−2⟹2(k−2)=−1(h−1)⟹h+2k=5...(i)

And

\begin{gathered} \underline\mathcal{ \bigstar \: Slope \: \: of \: \: Line \: \: L_2 \: \:joining } \\ \underline\mathcal{ points \: \: (h , k) \: and \: \: (4,3) \: \: is} \\ \\ \sf m_2 = \frac{3 - k}{4 - h} \\ \\ \end{gathered}★SlopeofLineL2joiningpoints(h,k)and(4,3)ism2=4−h3−k

\huge \mathcal{As}As

\begin{gathered} \underline\mathcal{ \maltese \: Line \: \: L_1 \: \: and \: \: L_2 \: \: are \: \: } \\ \\ \underline\mathcal{ perpendicular \: \: to \: \: each \: \: other}\end{gathered}✠LineL1andL2areperpendiculartoeachother

\therefore \: m_1m_2 = - 1∴m1m2=−1

\begin{gathered}( - \dfrac{1}{2} ) ( \dfrac{3 - k}{4 - h} ) = - 1 \\ \\ \implies \boxed{\boxed{\bf2h - k = 5}} ...(ii)\end{gathered}(−21)(4−h3−k)=−1⟹2h−k=5...(ii)

Solving (i) and (ii) we get

(h,k) = (3,1)

\bf \dfrac{k}{h} = \dfrac{1}{3}hk=31

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