Answer:
Part a) The slope of the hypotenuse of triangle ABC is [tex]m_A_B=-1.5[/tex]
Part b) The coordinates of point R are (4,-7)
Step-by-step explanation:
Part a) What is the slope of the hypotenuse of triangle ABC?
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
The hypotenuse of triangle ABC is the segment AB
we have
A(-6, 8) and B(-2, 2)
substitute the values
[tex]m_A_B=\frac{2-8}{-2+6}[/tex]
[tex]m_A_B=\frac{-6}{4}[/tex]
[tex]m_A_B=-\frac{3}{2}[/tex]
Part b) What are the coordinates of the hypotenuse of triangle QRS? Q(2, -4) and R( _, _ )
we know that
If triangle ABC and triangle QRS are similar, then the ratio of its corresponding sides is proportional, the slope of its corresponding sides are congruent and its corresponding interior angles are congruent too.
so
[tex]m_Q_R=m_A_B[/tex]
[tex]m_Q_R=-\frac{3}{2}[/tex]
we have
Q(2, -4) and R( x,y )
substitute in the formula of slope
[tex]-\frac{3}{2}=\frac{y+4}{x-2}[/tex]
Remember that Triangle ABC and triangle QRS are the same orientation
so
The x-coordinate of R must be positive
The y-coordinate of R must be negative
Plot points A,B and Q to understand
therefore
[tex]-3=y+4[/tex] ----> [tex]y=-7[/tex]
[tex]2=x-2[/tex] ----> [tex]x=4[/tex]
The coordinates of point R are (4,-7)
Answer:
What is the slope of the hypotenuse of triangle ABC?
-3/2
What are the coordinates of the hypotenuse of triangle QRS?
Q(2, -4) and R(4, -7)
Have a good day.
