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Using slope, show that a(1,1), b(10,4), and c(7,7) are the vertices of a right triangle

User Will Ayd
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2 Answers

6 votes
  • Slope of AC×Slope of BC=-1


\\ \rm\hookrightarrow (7-1)/(7-1)* (7-4)/(7-10)=-1


\\ \rm\hookrightarrow (6)/(6)* (3)/(-3)=-1


\\ \rm\hookrightarrow 1(-1)=-1

Hence they are vertices of right angled triangle

C is the right angle

User Salviati
by
8.9k points
6 votes

Answer:

Determine the slopes (gradients) of each line.

If the slopes of two of the lines are negative reciprocals (if their product is -1), the lines are perpendicular (the vertex is 90°).

Using slope formula:
m=(y_2-y_1)/(x_2-x_1)

Slope of AC:

A = (1, 1) =
(x_1,y_1)

C = (7, 7) =
(x_2,y_2)


m=(y_2-y_1)/(x_2-x_1)=(7-1)/(7-1)=1

Slope of AB:

A = (1, 1) =
(x_1,y_1)

B = (10, 4) =
(x_2,y_2)


m=(y_2-y_1)/(x_2-x_1)=(4-1)/(10-1)=\frac13

Slope of BC:

B = (10, 4) =
(x_1,y_1)

C = (7, 7) =
(x_2,y_2)


m=(y_2-y_1)/(x_2-x_1)=(7-4)/(7-10)=-1

Therefore, as AC and BC are negative reciprocals of each other (1 x -1 = -1), m∠C = 90° which proves that the triangle is a right triangle.

User Dancl
by
7.9k points

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