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This is one of our many quizzes on Vertical translations. Click on this to access more such competitive quizzes on Functions.

Vertical translations Quiz 2

mathematics

 If a point $A(35,27)$ is vertically translated by $27$ units, then find the new coordinates of the point?

 If a point $A(h,k)$ is vertically translated by a unit, then the new coordinates are $A(h,k+a)$.

  The point $A(35,27)$ is vertically translated by $27$ units.  $ \\ $ Then the y-coordinate of new point $=27+27=54$ $ \\ $ So, the new coordinates when $A(35,27)$ is vertically translated are $B(35,54)$.

 Find the vertical translation if the point is $\text{A(92,79)}$ translated to $\text{B(27,192)}$?

 The difference between the y-coordinates of the translated point to the original point gives the value of vertical translation.

  Let us assume the value of vertical translation is equal to $x$. $ \\ x=192-79=113 \\ $ So, the value of $x$ is equal to $113$.

 Find the vertical translation if the point is $\text{A(}{{\text{r}}^{2}}\text{,r)}$ translated to $\text{B(27,2+3}{{\text{r}}^{3}}\text{)}$ such that the vertical translation is minimum $(r > 0)$?

 If a graph is said to be vertically translated, then it is clear that the distance between each and every element is the same.

Let us assume the value of vertical translation is equal to $x$  $ \\ x=3{{r}^{3}}+2-r......(1) \\ $ It is given that the vertical translation is minimum. $ \\   \dfrac{dx}{dr}=\dfrac{d(3{{r}^{3}}+2-r)}{dr}=27{{r}^{2}}-1=0 \\  \Rightarrow r=\dfrac{1}{3\sqrt{3}}.....(2) \\ $ Now place equation $(2)$ in equation $(1)$, then we get $ \\ x=3{{\left( \dfrac{1}{3\sqrt{3}} \right)}^{3}}+2-\dfrac{1}{3\sqrt{3}} \\  \Rightarrow x=2-\dfrac{8}{3\sqrt{3}} \\ $

 The blue graph is translated into the green graph by k units. The green graph is translated into the red graph by m units. Now find the value of $|m-k-2|$? $ \\ $ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/6d100fd6-82fc-44f2-9a22-81b4154e23e76809000385530596561.png"/> 

 If a graph is said to be vertically translated, then it is clear that the distance between each and every element is the same. $ \\ $ The blue graph intersects the y-axis at $(0,3)$. $ \\ $ The green graph intersects the y-axis at $(0,4)$. $ \\ $ The red graph intersects the y-axis at $(0,5)$. $ \\ $ So, the value of $k$ is equal to $1$ and the value of m is equal to $1$. $ \\ |m-k-2|=|1-1-2|=2$

 Write the equation for the given graph. $ \\ $ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/db3d061b-b6f4-44c9-9b3e-7d999b7669124544840774318941693.png"/>

 From the graph, we have to find out the value of length of x-translation and y-translation. Now based on the values, we have to write the equation of the given graph.

 From the graph, it is clear that the graph similar to the graph of $|x|$. $ \\ $ So, it is clear that the graph is translated. $ \\ $ The graph of $|x|$ having a V-shape at $(0,0)$ and the given graph having a V-shape at $(-5,1)$. $ \\ $  So, we can say that the given graph is translated by $-5$ units by x-axis and $1$ units by y-axis. $ \\ $ So, the equation of the graph is $y-1=|x+5|$.