Triangle p is reflected in the line y = -x to give triangle q. Triangle q is reflected in the line x= -1 to give triangle r. describe fully the single transformation that maps triangle r to triangle p

The single transformation that maps triangle r to triangle p is +90° (countrer clockwise) rotation about the point (-1, 0)

Explanation:

The coordinates change from reflection across y = -x is given as follows;

p = (x, y) becomes q = (-y, -x)

The reflection across the line x = -1 = reflection across the y-axis at x = -1

Reflection across the y-axis gives;

(x, y) → (-x, y)

The reflection across the line x = -1  gives;

(x, y) → (-x - 1, y)

Therefore;

q = (-y, -x) becomes r = (y -1, -x)

Hence the total transformation is presented as follows;

p = (x, y) becomes r = (y -1, -x)

y = -1 - x

Rotation of a coordinate about a point

x' = x×cosθ - y×sinθ

y' = y×cosθ + x×sinθ

Whereby we rotate -90° about the point (-1, 0), we have;

x = x'×cos(-90) - y'×sin(-90) -1 = y' - 1

y = y'×cos(-90) + x'×sin(-90) + 0 = -x'

Therefore, the single transformation that maps triangle p to triangle r is -90° rotation about the point (-1, 0)

Conversely, the single transformation that maps triangle r to triangle p is 90° rotation about the point (-1, 0).

Volcano forms as an oceanic plate moves across a hot spot.

Explanation:

When lava is poured out from the crack which appears in the floors of the ocean, this leads to the formation of the new mountains. When magma comes out of the crust of the surface and reaches on the top at the surface.

This leads to the formation of a volcano from the hot spot which is a location on the surface of earth from where the heat comes up from the deep inside the earth melting the rocks and then this melt comes up from the cracks and form volcanoes.