Question

determine the vertex which contain a right angle in triangle abc where A(4, - 2) B(7, 9 )and C( 7 - 2)

Answer 1

Answer:

Step-by-step explanation:

At point C

Answer 2

Answer:

The vertex C(7,-2)  contain a right angle in triangle ABC.

Step-by-step explanation:

The vertices of triangle ABC are A(4, - 2) B(7, 9 )and C( 7,- 2).

The slope formula is

$m=\frac{y_2-y_1}{x_2-x_1}$

$m_{AB}=\frac{9-(-2)}{7-4}=\frac{11}{3}$

$m_{BC}=\frac{-2-9}{7-7}=\infty$

Since the slope is undefined, therefore BC is a vertical line.

$m_{AC}=\frac{-2-(-2)}{7-4}=0$

Since the slope is 0, therefore AC is a horizontal line.

Vertical and horizontal lines are perpendicular to each other. So, the line BC and AC are perpendicular to each other.

The lines AC and BC intersect on C, so the angle C is a right angle.

$\angle C=90^{\circ}$

Therefore vertex C(7,-2)  contain a right angle in triangle ABC.