Question

ABC is a triangle in which D and E are the mid-points of the sides AB and AC respectively. If the coordinates of D and E are (-1,3)and (3,-1)respectively, then the length of the side BC of the triangle is:

Answer 1

Step-by-step explanation:

by distance formulae:

=

$\sqrt{(x2 - x1) {}^{2} + (y2 - y1) {}^{2} }$

here points are D(-1,3)&E(3,-1)

therefore DE=

$\sqrt{(3 - ( - 1)) {}^{2} + ( - 1 - 3) {}^{2} }$

$\sqrt{(4) {}^{2} + ( - 4) {}^{2} }$

$\sqrt{16 + 16}$

$\sqrt{32} = 4 \sqrt{2} units$

we know that the DE= 1/2BC

now,BC= 2(DE)

BC = 2× 4√2= 8√2units