What is the name of the transformation in which each point on a figure is turned through a given angle and direction around a given point?

The name of transformation is rotation.

Step-by-step explanation:

A rotation is a transformation that turns a figure about a fixed point called the center of rotation.  assume a positive angle of rotation turns the figure counterclockwise, and a negative angle turns the figure clockwise.

Hence, each of the point in the figure also get transformed by the same angle.

Example: Rotate the rectangle ABCD 90° clockwise about the point (0,-1).

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.