Proving the statement LJ = JT using the midpoint formula and distance formula.

IF J is the midpoint of segment LT, then LJ = JT

Definition of Midpoint

Given that point J is the midpoint of segment LT. That means LJ and JT are two line segments that are equal in length.

To prove this statement mathematically, we can use the midpoint formula. The midpoint formula states that the midpoint of a line segment with endpoints (x1,y1) and (x2,y2) is:

((x1 + x2)/2 , (y1 + y2)/2)

Let’s apply this formula to the endpoints of segment LT.

Let L = (x1,y1) and T = (x2,y2)

Then the midpoint J = ((x1 + x2)/2 , (y1 + y2)/2)

Since J is the midpoint of segment LT, we know that LJ and JT are equal in length.

We can use the distance formula to prove that LJ = JT.

Distance formula for LJ:

LJ = √((x2 – x1)/2)^2 + ((y2 – y1)/2)^2

Simplifying this:
LJ = √((x2 – x1)^2 + (y2 – y1)^2)/2

Distance formula for JT:

JT = √((x2 – x1)/2)^2 + ((y2 – y1)/2)^2

Simplifying this:
JT = √((x2 – x1)^2 + (y2 – y1)^2)/2

We can see from these formulas that LJ and JT are equal, so we can finally state that:

LJ = JT

Therefore, the statement is true and we have proven mathematically that if J is the midpoint of segment LT, then LJ = JT.

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