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zepelin [54]
3 years ago
5

A triangle with the coordinates (6,4), (2,-1), and (-3,5) is translated 4 Units left and rotate 180 degrees about the origin. Wh

at are the coordinates of the image.
Mathematics
1 answer:
ankoles [38]3 years ago
8 0

Answer:

(-2,-4),(2,1), and (7,-5)

Step-by-step explanation:

The given triangle has coordinates (6,4), (2,-1), and (-3,5).

When we translate 4 units left, the we obtain:

(6,4)------>(6-4,4)=(2,4)

(2,-1)----->(2-4,-1)=(-2,-1)

(-3,5)----->(-3-4,5)=(-7,5)

When the resulting figure is rotated 180° about the origin, the coordinates of the final figure becomes

(2,4)------>(-2,-4)

(-2,-1)----->(2,1)

(-7,5)------->(7,-5)

NB: The mapping for 180° rotation is:

(x,y)----->(-x,-y)

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hello

the points given are (-4, 47) and (2, -16)

let's find the intercept of this equation

\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ x_2=2 \\ y_2=-16 \\ y_1=47 \\ x_1=-4 \end{gathered}\begin{gathered} m=\frac{-16-47}{2-(-4)} \\ m=-\frac{21}{2} \\ slope=-\frac{21}{2} \end{gathered}

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\begin{gathered} x=2 \\ y=-16 \\ y=mx+c \\ m=-\frac{21}{2} \\ -16=-\frac{21}{2}(2)+c \\ -16=-21+c \\ \text{collect like terms} \\ c=-16+21 \\ c=5 \end{gathered}

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let's use this to write equation of the straight line

\begin{gathered} y=mx+c \\ y=-\frac{21}{2}x+5 \end{gathered}

from the calculations above, the equation of the straight line is given as y = -21/2x + 5

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