Which transformation will map figure l onto figure l'?

two congruent triangles figure l and figure l prime are drawn on a coordinate grid. figure l has vertices at negative 4, 2, negative 2, 4, and negative 3, 7. figure l prime has vertices at 2, 2, 4, 4, and 3, 7
horizontal translation of 8 units
horizontal translation of 6 units
reflection across x-axis
reflection across y-axis

Option b is right answer.

Horizontal translation of 6 units

Step-by-step explanation:

Given that L and L' are congruent triangles.

. Figure L has vertices at negative 4, 2, negative 2, 4, and negative 3, 7. Figure L prime has vertices at 2, 2, 4, 4, and 3, 7

On comparison of corresponding vertices we find that y coordinate remains the same for all vertices.

But x coordinate -4 became 2, -2 became 4, and -3 became 3.

This means original x coordinate is increased by 6 units to get L'

i.e. there is a horizontal translation of 6 units.

This will only make (-4,2) to (2,2),  (-2,4) to (4,4) and (-3,7) to (3,7)

Option b is right answer.

Horizontal translation of 6 units

let's call the solutions x₁ = (5 - 2√7)/3 and x₂ = (5 + 2√7)/3

then the equation is (x-x₁)(x-x₂) = 0

if you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.

step-by-step explanation:

you can see that a=1 (there is just an x²)

b = (-5 -2√7 + 2√7 - 5)/3 = -10/3

c = -2√7)/3 ) * (-5+2√7)/3) = -1/3

so your answer is 3x^2 – 10x – 1 = 0