Prove that the median to the hypotenuse of a right triangle is half the hypotenuse.
plan: since midpoints will be involved, use multiples of __ to name the coordinates for m and n.

D. 2

Step-by-step explanation:

Since midpoints will be involved, use multiples of 2 to name the coordinates for M and N.

Let

Then the midpoint P coordinates are

Use distance formula to find OP and MN:

So,

MN=2OP

or

OP=1/2 MN

The correct option is D.

Step-by-step explanation:

Given: ΔMNO is a right angled triangle with right angle ∠MON, P is midpoint of MN.

To prove:

Since midpoints will be involved, use multiples of _2_ to name the coordinates for M and N.

Let the coordinates for M and N are (0,2m) and (2n,0) receptively.

Midpoint formula:

The coordinates of P are

The coordinates of P are (n,m).

Distance formula:

Using distance formula, the distance between O(0,0) and P(n,m) is

Using distance formula, the distance between M(0,2m) and N(2n,0) is

On further simplification we get

Divide both sides by 2.

Interchange the sides.

Hence proved.

Therefore, the correct option is D.

we need the options

step-by-step explanation: