Triangle LMN with vertices L(0, 3), M(3, 4), and N(1, 2): a) 180° rotation about the origin b) dilation with scale factor of 2 using the origin as the center

Step-by-step explanation:

Given

Required

Determine the new coordinates of L, M and N

Applying (a): 180 degrees rotation about the origin

When is rotated about 180 degrees, the new point becomes

So:

==>

==>

==>

Applying (b): Dilation of scale factor, 2

The formula to apply here is;

So:

becomes:

becomes:

Hence;

The new coordinates are:

christopher is 272,195 year old

step-by-step explanation:

answer: the angel abc is 30°,and the abc is a triangle where the angel bac is 90°

so ac is the half of 24=12ft,and from the pythagorean theorem we find ba

ba=√bc^2-ac^2=√576-144=√432=12√3ft

so bac is 12+12√3=12(1+√3)ft