Prove that the median to the hypotenuse of a right triangle is half the hypotenuse. Proof: By the Distance Formula, MN = _. Therefore, OP=1/2 MN.

Option (A).

Step-by-step explanation:

From the figure attached,

ΔMON is a right triangle and coordinates of the points M and N are M(0, 2b) and N(2a, 0).

Coordinates of midpoint P →

                                            → (a, b)

From the formula of the distance between two points,

d =

MN =

      =

      = 2

Similarly, OP =

                     =

Therefore, OP =

and MN = = 2

Option (a) is the answer.

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

source:

add an image

step-by-step explanation: