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( _, _ )

Part a) The slope of the hypotenuse of triangle ABC is

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

The hypotenuse of triangle ABC is the segment AB

we have

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

substitute the values

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

we have

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

substitute in the formula of slope

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

---->

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