Question

In the graph below, line k with equation y = -k makes a 45° angle with the x- and y- axes.

Complete the following:

Rx Rk : (2,5)

(-2, -5)
(2, -5)
(-5, 2)

Answer 1

Given Equation of line is, y= -k, passing through Origin and making an angle of 45° with the positive direction of x axis is given by

k=tan 45°

k=1

So, the equation of line will be→y= -x.

Point (2,5) is reflected through x axis.So, Coordinates of point after reflection will be (-2,5).

→Now, the point is reflected through line, y=-x.So, This reflection rule says

(x,y)→(-y,-x).

→Now, when point (-2,5) is reflected through line, y=-x the coordinates of point after reflection will be

= (-5, 2)

Option B

Answer 2

D. (-5,2)

Explanation:

1st reflection = reflection across the line k with the rule:

(x,y)→(-y,-x)

So,

(2,5)→(-5,-2)

2nd reflection = reflection across the x-axis with the rule

(x,y)→(x,-y)

So,

(-5,-2)→(-5,2)

After two consecutive reflections

(2,5)→(5,2)