The image of (2,3) w.r.t y-axis is collinear with (-1,-1) and (-4,
x), then x=
Answers
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) :
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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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
Hence the required value of x = 11
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