Math, asked by Nita430, 11 months ago

The image of (2,3) w.r.t y-axis is collinear with (-1,-1) and (-4,
x), then x=​

Answers

Answered by QwertyPs
18

Image of (2,3) w.r.t y-axis is (-2,3)

Now points are (-2,3) , (-1,-1) and (-4,x)

Equation of line with points (-2,3) and (-1,-1) :

\frac{y-y_1}{x-x_1} = \frac{y_2-y_1}{x_2-x_1} \\ \frac{y-3}{x+2}= \frac{-1-3}{-1+2} \\ \frac{y-3}{x+2}=\frac{-4}{1} \\  y-3 = -4x - 8\\ 4x + y + 5=0

Equation of line = 4x + y + 5 = 0

Since all three points are collinear, (-4,x) should lie on the line, thus satisfying the equation.

Putting (-4,x) in the equation

-16 + x + 5 =0

x - 11 = 0

x = 11

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Answered by pulakmath007
4

The value of x = 11

Given :

The image of (2,3) w.r.t y-axis is collinear with (-1,-1) and (-4,x)

To find :

The value of x

Solution :

Step 1 of 2 :

Find the image of (2,3) w.r.t y-axis

We know that for a given point (a, b) the image of (a, b) with respect to y axis is ( - a, b)

Thus for the given point (2,3) , the image of (2,3) with respect to y axis is ( - 2,3)

Step 2 of 2 :

Find the value of the x

It is given that the image of (2,3) w.r.t y-axis is collinear with (-1,-1) and (-4,x)

∴ (- 2,3) is collinear with (-1,-1) and (-4,x)

∴ The area of the triangle formed by the points (- 2,3) is collinear with (-1,-1) and (-4,x) is 0

\displaystyle \sf{ \implies  \frac{1}{2}  | -  2( - 1 - x)  - 1(x  - 3) - 4(3  + 1)|  = 0}

\displaystyle \sf{ \implies  \frac{1}{2}  |2 + 2x  - x + 3 - 16|  = 0}

\displaystyle \sf{ \implies  \frac{1}{2}  |x - 11|  = 0}

\displaystyle \sf{ \implies  x  - 11 = 0}

\displaystyle \sf{ \implies  x = 11}

Hence the required value of x = 11

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