A line segment has endpoints at $(1 ,2 )$ and $(3 , 1)$ . The line segment is dilated by a factor of $4$ around $(2 , 3)$ . 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 $(-2, -1)$ and $(6, -5)$
Length $l=8.94427" "$

Let $A(x_a, y_a)=(1, 2)$
Let $B(x_b, y_b)=(3, 1)$
Let $R(x_r, y_r)=(2, 3)$

Let the new endpoints be
$C(x_c, y_c)$ and $D(x_d, y_d)$

Let $k=4$

Solve the new endpoints by ratio and proportion

$(RC)/(RA)=k$

$(x_c-x_r)/(x_a-x_r)=4$
$(x_c-2)/(1-2)=4$

$x_c=-2$

$(y_c-y_r)/(y_a-y_r)=4$
$(y_c-3)/(2-3)=4$

$y_c=-1$

$(RD)/(RB)=k$
$(x_d-x_r)/(x_b-x_r)=4$
$(x_d-2)/(3-2)=4$
$x_d=6$

$(y_d-y_r)/(y_b-y_r)=4$
$(y_d-3)/(1-3)=4$
$y_d=-5$

Length

$l=sqrt((x_d-x_c)^2+(y_d-y_c)^2)$
$l=4sqrt(5)=8.94427" "$

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

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?