What is the image of (2,3)(2,3) after a reflection over the line y=-xy=−x?

The image of (2,3) after a reflection over the given line will be: (-3,-2)

Step-by-step explanation:

The given point is (2,3)

Let (x,y) be a point, when it will be reflected over the line y=-x the coordinates are exchanged and are negated i.e. point (x,y) becomes (-y,-x)

When a point is reflected over a line the distance between the image of point and the line remains the same as the distance between original point and line.

Given point will become: (-3,-2)

Hence,

The image of (2,3) after a reflection over the given line will be: (-3,-2)

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this