Triangle A″B″C″ is formed by a reflection over x = −1 and dilation by a scale factor of 4 from the origin. Which equation shows the correct relationship between ΔABC and ΔA″B″C″? A) segment A double prime B double prime equals four segment BC B) segment BC equals 4 segment A double prime B double prime C) segment AB over segment A double prime B double prime equals one fourth D) segment C double prime A double prime over segment CA equals one fourth

The correct option is;

C. Segment AB over segment A double prime B double prime equals one fourth.

Step-by-step explanation:

The given information are;

A''B''C'' is formed by the reflection of ABC over x = -1 and the dilation by a factor of 4;

We have;

A(-3, 3)

B(1, -3)

C(-3, -3)

Reflection of the pre-image gives;

Reflect,                     Across x = -1

A(-3, 3),              →        A'(1, 3)

B(1, -3),               →        B'(-3, -3)

C(-3, -3),             →        C'(1, -3)

Length of segment AB = √((1 - (-3))² + (-3  -3)²) = 7.2

Dilation by 4 gives;

A'(1, 3)                 →        A''(4, 12),

B'(-3, -3)              →        B''(-12, -12),

C'(1, -3)                →        C''(4, -12),

Length of segment A''B'' = √((4 - (-12))² + (12 - (-12))²) = 28.84

Therefore, AB/(A''B'') = 7.2/28.84 = 1/4

Which gives the correct option as C. Segment AB over segment A double prime B double prime equals one fourth.

side xy = 10

sin(x) = 4/5

cos(x) = 3/5

tan(x) = 4/3

step-by-step explanation:

sss (side, side, side)

sas (side, angle, side)

asa (angle, side, angle)

aas (angle, angle, side)

hl (hypotenuse, leg)