4) The given figure shows ∆ABC. Points D, E and F are the mid-points of sides AB, AC and BC respectively. Sides AB, BC and CA measure 6 cm, 10 cm and 8 cm respectively. What is the area of ∆DEF? *

the area of ∆DEF = 6 cm²

Step-by-step explanation:

The midpoint theorem states that the line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side.

DE // BC and DE = BC/2 = 10/2 = 5

same reason: DF = AC/2 = 4

FE = AB/2 = 3

DF² + FE² = 16 + 9 = 25 = 5² = DE²

by the Pythagorean theorem, ΔDFE is a right triangle

area ΔDEF = (3 x 4) / 2 = 6 cm²

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1