Question

Triangle ABC and triangle QRS are similar and are the same orientation. The endpoints of the hypotenuse of triangle ABC are A(-6, 8) and B(-2, 2). The hypotenuse of triangle QRS is on the same line as the hypotenuse of triangle ABC and is one-half the length of AB.

What is the slope of the hypotenuse of triangle ABC? __________________

What are the coordinates of the hypotenuse of triangle QRS? Q(2, -4) and R( _, _ )

Answer 1

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.

Answer 2

Part a) The slope of the hypotenuse of triangle ABC is
`m_A_B=-1.5`

Part b) The coordinates of point R are (4,-7)

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

`m=(y2-y1)/(x2-x1)`

The hypotenuse of triangle ABC is the segment AB

we have

A(-6, 8) and B(-2, 2)

substitute the values

`m_A_B=(2-8)/(-2+6)`

`m_A_B=(-6)/(4)`

`m_A_B=-(3)/(2)`

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

`m_Q_R=m_A_B`

`m_Q_R=-(3)/(2)`

we have

Q(2, -4) and R( x,y )

substitute in the formula of slope

`-(3)/(2)=(y+4)/(x-2)`

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

`-3=y+4` ---->
`y=-7`

`2=x-2` ---->
`x=4`

The coordinates of point R are (4,-7)