A line segment has endpoints at $(1, 2)$ $(1 ,2 )$ and $(3, 1)$ $(3 , 1)$ . The line segment is dilated by a factor of $4$ $4$ around $(2, 3)$ $(2 , 3)$ . What are the new endpoints and length of the line segment?

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A line segment has endpoints at $(1, 2)$ $(1 ,2 )$ and $(3, 1)$ $(3 , 1)$ . The line segment is dilated by a factor of $4$ $4$ around $(2, 3)$ $(2 , 3)$ . What are the new endpoints and length of the line segment?

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Answer 1 · 2016-04-07T08:38:03

New Endpoints are $(- 2, - 1)$ $(-2, -1)$ and $(6, - 5)$ $(6, -5)$
Length $l = 8.94427$ $l=8.94427" "$

Explanation:

Let $A (x_{a}, y_{a}) = (1, 2)$ $A(x_a, y_a)=(1, 2)$
Let $B (x_{b}, y_{b}) = (3, 1)$ $B(x_b, y_b)=(3, 1)$
Let $R (x_{r}, y_{r}) = (2, 3)$ $R(x_r, y_r)=(2, 3)$

Let the new endpoints be
$C (x_{c}, y_{c})$ $C(x_c, y_c)$ and $D (x_{d}, y_{d})$ $D(x_d, y_d)$

Let $k = 4$ $k=4$

Solve the new endpoints by ratio and proportion

$\frac{R C}{R A} = k$ $(RC)/(RA)=k$

$\frac{x_{c} - x_{r}}{x_{a} - x_{r}} = 4$ $(x_c-x_r)/(x_a-x_r)=4$
$\frac{x_{c} - 2}{1 - 2} = 4$ $(x_c-2)/(1-2)=4$

$x_{c} = - 2$ $x_c=-2$

$\frac{y_{c} - y_{r}}{y_{a} - y_{r}} = 4$ $(y_c-y_r)/(y_a-y_r)=4$
$\frac{y_{c} - 3}{2 - 3} = 4$ $(y_c-3)/(2-3)=4$

$y_{c} = - 1$ $y_c=-1$

$\frac{R D}{R B} = k$ $(RD)/(RB)=k$
$\frac{x_{d} - x_{r}}{x_{b} - x_{r}} = 4$ $(x_d-x_r)/(x_b-x_r)=4$
$\frac{x_{d} - 2}{3 - 2} = 4$ $(x_d-2)/(3-2)=4$
$x_{d} = 6$ $x_d=6$

$\frac{y_{d} - y_{r}}{y_{b} - y_{r}} = 4$ $(y_d-y_r)/(y_b-y_r)=4$
$\frac{y_{d} - 3}{1 - 3} = 4$ $(y_d-3)/(1-3)=4$
$y_{d} = - 5$ $y_d=-5$

Length

$l = \sqrt{{(x_{d} - x_{c})}_{d}^{2} + {(y_{d} - y_{c})}_{d}^{2}}$ $l=sqrt((x_d-x_c)^2+(y_d-y_c)^2)$
$l = 4 \sqrt{5} = 8.94427$ $l=4sqrt(5)=8.94427" "$

God bless....I hope the explanation is useful

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A line segment has endpoints at $(1, 2)$ $(1 ,2 )$ and $(3, 1)$ $(3 , 1)$ . The line segment is dilated by a factor of $4$ $4$ around $(2, 3)$ $(2 , 3)$ . What are the new endpoints and length of the line segment?

1 Answer

Explanation:

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A line segment has endpoints at (1 ,2 )(1,2)(1 ,2 ) and (3 , 1)(3,1)(3 , 1). The line segment is dilated by a factor of 4 44 around (2 , 3)(2,3)(2 , 3). What are the new endpoints and length of the line segment?

1 Answer

Explanation:

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A line segment has endpoints at $(1, 2)$ $(1 ,2 )$ and $(3, 1)$ $(3 , 1)$ . The line segment is dilated by a factor of $4$ $4$ around $(2, 3)$ $(2 , 3)$ . What are the new endpoints and length of the line segment?