Question

Triangle EFG has vertices E(–3, 4), F(–5, –1), and G(1, 1). The triangle is translated so that the coordinates of the image are E’(–1, 0), F’(–3, –5), and G’(3, –3).

Answer 1

The rule that was  used to translate the image Triangle EFG to E'F'G' is

T2,-4(x,y)

Given :

• Triangle EFG has vertices E(–3, 4), F(–5, –1), and G(1, 1).

• The coordinates of the image after being translated are E’(–1, 0), F’(–3, –5), and G’(3, –3)

To find out the rule, we need to check the coordinates E  and E'

E is (-3,4)  and E' is (-1,0)

-3 + x = -1

x = -1 +3

   = 2

4 + y = 0

y = 4

So, we can say that 2 is added with x  and 4 is subtracted from y  to get E'

Let's check with F and F'

F(–5, –1)  and F’(–3, –5)

-5+2=-3

-1-4=-5

So the rule used to translate the image is T2,-4(x,y)

A triangle is a polygon with three sides and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C are represented as triangle ABC.

In Euclidean geometry, any three points, if not collinear, define a unique triangle and, at the same time, a unique plane (that is, two-dimensional Euclidean space). This means that there is only one plane containing this triangle, and all triangles are contained in one plane. If all geometries were just Euclidean planes, there would be only one plane and all triangles would be in it. But this is not the case in high-dimensional Euclidean space.

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