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mamaluj [8]
3 years ago
14

What are the new vertices of triangle QRS, shown, if the triangle is reflected across the line y = x, also shown? Question 6 opt

ions: A) Q′ = (–2,–3), R′ = (1,1), S′ = (2,–1) B) Q′ = (2,–4), R′ = (4,0), S′ = (3,–1) C) Q′ = (2,–5), R′ = (5,0), S′ = (2,–1) D) Q′ = (5,2), R′ = (0,5), S′ = (1,2)

Mathematics
1 answer:
ExtremeBDS [4]3 years ago
6 0

Answer:

C

Step-by-step explanation:

Under a reflection in the line y = x

a point (x, y ) → (y, x ) , thus

Q(- 5, 2 ) → Q'(2, - 5 )

R(0, 5 ) → R'(5, 0 )

S(- 1, 2 ) → S'(2, - 1 )

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Complete the given diagram by dragging expressions to each leg of the triangle. Then, correctly complete the equation to derive
Nimfa-mama [501]

The equation to derive the distance d is \sqrt{(x2-x1)^2+(y2-y1)^2}. The lengths of the other legs of the given triangle are (y2 - y1) and (x2 - x1).

<h3>What is the formula for calculating the distance between two points?</h3>

Consider the two points (x1, y1) and (x2, y2)

The formula used for calculating the distance between the two points is

distance = \sqrt{(x2-x1)^2+(y2-y1)^2}

<h3>Calculation:</h3>

Given that,

The triangle in the graph has vertices (x1, y1), (x2, y2), and (x2, y1)

Since this triangle makes 90°, it is a right-angled triangle.

Hypotenuse = (x1, y1) to (x2, y2), Adjacent = (x1, y1) to (x2,y1), and Opposite = (x2, y1) to (x2, y2).

Consider the length of the hypotenuse = d

So, using the distance formula, the length of the hypotenuse(d) is,

d = \sqrt{(x2-x1)^2+(y2-y1)^2}

And the lengths of the other two legs of the given triangle are,

Length of the adjacent side: (x1, y1) to (x2,y1)

= \sqrt{(x2-x1)^2+(y1-y1)^2}

= \sqrt{(x2-x1)^2+0}

= (x2-x1)

Length of the opposite side: (x2, y1) to (x2, y2)

= \sqrt{(x2-x2)^2+(y2-y1)^2}

= \sqrt{0+(y2-y1)^2}

= (y2-y1)

Therefore, the derived distances for the given triangle are:

d=\sqrt{(x2-x1)^2+(y2-y1)^2}, (x2 - x1), and (y2 - y1).

Learn more about the distance between two points here:

brainly.com/question/661229

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