Find 3 numbers that have
median = 5
mean = 5
AND range=4

question says to graph a triangle (xyz) and reflect it over the line y=x to create triangle x'y'z'.

we know that line y=x has both coordinates equal like (1,1), (5,5) etc so we can easily graph that reflecting line.

description of transformation:

we can see that x and y coordinate gets switched after transformation like (2,8) changed to (8,2)

what do you notice about the two line segments you drew:

we see that line segments xp and x'p are of same length and perpendicular to the reflecting line y=x.

do you think you would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line? :

yes, i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line.

how do you know? :

by measuring the length of yk and y'k.

ok , let me start from the meaning of word translation .

translation means moving an object by a certain distance in any direction.

the nature of the object i.e shape, size does not change. neither the figure is

reflected, nor rotated.

as δ abc is translated, it is not given it is translated in which direction

so,(2,-7) lies in fourth quadrant.

if translation of t units is applied to the coordinates of b (2,-7) i.e x in right direction,and y in up   then new coordinates, b'=(2+t, -7+t)

if translation of t units is applied to the coordinates of b(2,-7) i.e x in right direction,and y in down   then new coordinates, b'=(2+t, -7-t)

if translation of t units is applied to the coordinates of b(2,-7) i.e x in left direction,and y in up   then new coordinates, b'=(2-t, -7+t)

if translation of t units is applied to the coordinates of b(2,-7) i.e x in left direction,and y in down   then new coordinates, b'=(2-t, -7-t)