Question

What is the image of the point (2, 3) in the line y = - x ?

• A. (- 3, - 2)
• B. (- 3, 2)
• C. (- 2, - 3)
• D. (3, 2)

Answer 1

Answer: (A)

(- 3, - 2)

Answer 2

Let there be a point P(2,3) on cartesian plane. Image of this point in the line y = -x will lie on a line which is perpendicular to this line and distance of this point from y = -x will be equal to distance of the image from this line. Let Q be the image of p and let the co-ordinate of Q be (b, k) Slope of line y = -x is -1 Line joining P, Q will be perpendicular to y = -x so, its slope = 1. Let the equation of the line be y = x + c since this passes through point (2, 3) 3 = 2 + c $\rightarrow$ c = 1 and the equation y = x + 1 The point of intersection R lies in the middle of P & Point of intersection of line y = - x and y = x + 1 is $2 y = 1 , \Rightarrow \, y = \frac{1}{2}$ and $x = - \frac{1}{2}$ Hence, $\frac{h +2}{2} = - \frac{1}{2}$ and $\frac{k + 3}{2} = \frac{1}{2}$ $\Rightarrow \, h = -3$ and $k = - 2$ So, the image of the point (2, 3) in the y = - x is ( -3, -2).