Question

Triangle END is translated using the rule (x,y)→(x−4, y−1) to create triangle E'N'D'. If a line segment is drawn from point E to point E' and from point N to point N',

which statement would best describe the line segments drawn?

A. They are parallel and congruent.
B. They are perpendicular to each other.
C. They share the same midpoints.
D. They create diameters of concentric circles.

Answer 1

@563blackghost

Answer 2

@Kevin

Answer 3

Here is an example of your question with the translation of two points....What do the line segments look like?

Answer 4

pls wait :)

Answer 5

@563blackghost PARALLEL!

Answer 6

Find the gradient of the line segment :

m =
y1 - y2
------- =
x1 - x2

0-(-1)
------ =
0-(-4)

1/4

For first triangle END :
y - y1 = m (x - x1)
y - 0 = 1/4(x-0)
y = 1/4x

For triangle that was translated :
y - y1 = m (x - x1)
y - (-1) = 1/4(x - (-4))
y + 1 = 1/4 (x + 4)
y + 1 = 1/4 x + 1
y = 1/4x

As you can see here, the gradient of first triangle END and the triangle END that was translated is same. So they are parallel for every side and of course to both triangles itself.