What is the area, in square units, of ΔDEF with D(5,−1), E(1,−4), and F(−5,4)?

25 square units,
37.5 square units
50 square units,
75 square units
is it c?

The line DF is

y+1 = -1/2 (x-5)
or
x+2y-3=0
The distance from E to that line is |1-8-3|/√(1^2+2^2) = 10/√5
The length of DF is √(10^2+5^2) = 5√5
So the area of DEF is 1/2 * 5√5 * 10/√5 = 25

The answer is A. 25 square units.

bro when yall have the answers i love yall but this exam is not it 😓

ty "bruh" ily

To find the area of a triangle with coordinates of its vertices, you can use the Shoelace Formula.

The Shoelace Formula is a mathematical method that calculates the area of any polygon given the coordinates of its vertices. The formula is as follows:

area = |(x1*y2 + x2*y3 + x3*y1 - x2*y1 - x3*y2 - x1*y3)/2|

Using the coordinates of the vertices of triangle DEF, we can substitute them into the Shoelace Formula:

D(5, -1), E(1, -4), F(-5, 4)

Plugging in the values:

area = |((5 * -4) + (1 * 4) + (-5 * -1) - (1 * -1) - (-5 * -4) - (5 * 4))/2|

Simplifying:

area = |(-20 + 4 + 5 + 1 + 20 - 20)/2|

area = |(-10)/2|

area = |-5|

The absolute value of -5 is 5.

Therefore, the area of triangle DEF is 5 square units.

The correct option is not listed among the choices you provided.

no...did you sketch it?