Question

In the given below figure, in ∆ABC, D and E are the midpoint of the sides BC and AC
respectively. Find the length of DE. Prove that DE = 1/2AB

Answer 1

Answer:  Length of DE = 1 unit.

Step-by-step explanation:

Since we have given that

Coordinates of A is given by

$(-6,-1)$

Coordinates of B is given by

$(2,-2)$

Coordinates of C is given by

$(4,-2)$

As we have given that "D and E are the midpoints of the sides BC and AC."

So, by Using the "Mid -point " formula, we get,

$D=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\\\\D=(\frac{-6+2}{2},\frac{-1-2}{2})\\\\D=(-2,-1.5)\\\\similarly,\\\\E=(\frac{x_1+x_3}{2},\frac{y_1+y_3}{2})\\\\E=(\frac{-6+4}{2},\frac{-1-2}{2})\\\\E=(-1,-1.5)$

Now, we will use the formula of "Distance between two co-ordinates":

so, Distance between DE is given by

$DE=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\DE=\sqrt{(-2+1)^2+(-1.5+1.5)^2}\\\\DE=\sqrt{1^2}\\\\DE=1\ unit$

Similarly,

$BC=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\BC=\sqrt{((4-2)^2+(-2+2)^2}\\\\BC=\sqrt{2^2}\\\\BC=2\ unit$

So, we get our equality:

$DE=1=\frac{1}{2}\times 2=\frac{1}{2}\times BC\\\\DE=\frac{1}{2}BC$

Hence, Length of DE = 1 unit.

Hence proved.