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Byju's Answer

Standard XII

Mathematics

f(x) Transforms to f(-x)

Nick and Amy ...

Question

Nick and Amy are practicing graph translations by moving $y = 2 x$ on the coordinate plane. Nick moved the graph by $5$ units to the left and $a$ units downward and obtained $L_{1} .$ Amy moved the graph by $b$ units to the right and $3$ units upward and obtained $L_{2} .$ If $L_{1}$ and $L_{2}$ are graphically represented as shown in the diagram below,then value of $a + 2 b$ is

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Solution

Nick case:
Moving $y = 2 x$ by $5$ units to the left and $a$ units downward gives
$L_{1} : y = 2 (x + 5) - a$
As line $L_{1}$ passes through $(0, 7)$ , we get
$\Rightarrow 7 = 2 (0 + 5) - a \Rightarrow a = 3$

Amy case:
Moving $y = 2 x$ by $b$ units to the right and $3$ units upward gives
$L_{2} : y = 2 (x - b) + 3$
As line $L_{2}$ passes through $(3, 0)$ , we get
$\Rightarrow 0 = 2 (3 - b) + 3 \Rightarrow b = \frac{9}{2}$

$∴ a + 2 b = 3 + 9 = 12$

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Similar questions

Q. Nick and Amy are practicing graph translations by moving

y = 2 x

on the coordinate plane. Nick moved the graph by

5

units to the left and

a

units downward and obtained

L_{1} .

Amy moved the graph by

b

units to the right and

3

units upward and obtained

L_{2} .

L_{1}

and

L_{2}

are graphically represented as shown in the diagram below,then value of

a + 2 b

Q. Let

l_{1}

be parallel to

\frac{x}{5 / 3} + \frac{y}{5 / 4} = 1

and

l_{2}

be perpendicular to it. If

l_{1}

has

x -

intercept equals to

2

units and

l_{2}

has

y -

intercept equals to

2

units, then the absolute value of the ratio of

y -

intercept of

l_{1}

x -

intercept of

l_{2}

Q. A line

L_{1}

passes through the point

(1, 1)

and

(2, 0)

and another line

L_{2}

passes through

(\frac{1}{2}, 0)

and perpendicular to

L_{1} .

Then the area (in sq. units) of the triangle formed by the lines

L_{1},

L_{2}

and

y -

axis is

Q. A line

L_{1}

passes through the points

(1, 1)

and

(2, 0)

and another line

L_{2}

passes through

(\frac{1}{2}, 0)

and is perpendicular to

L_{1} .

If the area of the triangle formed by the line

L_{1}, L_{2}

and

y -

axis is

\frac{p}{q}

sq. units where

p, q

are co-prime, then value of

p + q

The point $(3, 2)$ is reflected in the y-axis and then moved a distance of 5 units towards the negative side of y-axis. The coordinates of the point thus obtained are

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f(x) Transforms to f(-x)

Standard XII Mathematics

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