The coordinates of the vertices of △def are d(−4, 1) , e(3, −1) , and f(−1, −4) . which statement correctly describes whether △def is a right triangle? △def is a right triangle because de⎯⎯⎯⎯⎯ is perpendicular to ef⎯⎯⎯⎯⎯ . △def is a right triangle because de⎯⎯⎯⎯⎯ is perpendicular to df⎯⎯⎯⎯⎯ . △def is a right triangle because df⎯⎯⎯⎯⎯ is perpendicular to ef⎯⎯⎯⎯⎯ . △def is not a right triangle because no two sides are perpendicular.

Solution-

We can solve this problem by using the concept of slope.

Slope of a line joining two points A (x1,y1) and B (x2,y2) is given by-

slope of AB= (y2-y1)÷(x2-x1)

We have given the vertices of a triangle as D(-4,1), E(3,-1) and F(-1,-4).

∴ slope of line joining D and E= (-1-1)÷(3-(-4))= -2/7

slope of line joining D and F= (-4-1)÷(-1-(-4))= -5/3

and  slope of line joining E and F= (-4-(-1))÷(-1-3)= 3/4

∵ Two lines are perpendicular to each other if product of their slopes= -1

Statement 1 is wrong because, (slope of DE)×(slope of EF)=(-2/7)×(3/4)=-3/14≠ -1

Statement 2 is wrong because, (slope of DE)×(slope of DF)=(-2/7)×(-5/3) =10/21≠ -1

Statement 3 is wrong because,(slope of DF)×(slope of EF)=(-5/3)×(3/4)= -5/4≠ -1

∴Statement 4 is correct.

△DEF is not a right triangle because no two sides are perpendicular.

Step-by-step explanation:

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