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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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Find the equation of the line that passes through points (3,5) and (-6,2). Write the equation in slope intercept form.
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                              = (5 -2) ÷ (3 - (-6))
                              = ¹/₃
   
     using the point-slope form (y-y₁) = m(x-x₁)
     using (3,5)
           (y - 5) = ¹/₃ (x -3)
             y - 5  = ¹/₃x - 1
        ⇒      <span>  y =   ¹/₃ x  + 4  [OPTION D]


</span>2)        y =  2x  +  5  .... (1)
<span>           </span>y = ¹/₂ x  + 6  .... (2)
       
         by substituting y in (1) for y in (2)

           2x  +  5 = ¹/₂ x  + 6 
                 ³/₂ x = 1
                      x = ²/₃

        by substituting found x (2)

            y = ¹/₂ (²/₃)  + 6
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∴ common point is (²/₃ , ¹⁹/₃)  thus answer is FALSE [OPTION B]


3) Yes [OPTION A]
     This is because the both have a gradient of 5 and if they have the same gradient then that means that the two lines are parallel to each other.

4) No [OPTION B]
       Two lines are perpendicular if their gradients multiply to give - 1 and as such one is the negative reciprocal of the other.  Since both gradients are ¹/₂ then they are actually parallel and not perpendicular.

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Hope this helps, have a great day/night!

~IFoundJiminsLostJams~

Step-by-step explanation:

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Answer:

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