Write the coordinate of the vertices after a translation 8 units left and 13 units down. S(0,10). T(8,10) U(1,5)

S'(-8 , -3)

T'(0 , -3)

U'(-7 , -8)

Step-by-step explanation:

Note that points are (x , y).

When you are translating to the left, you are subtracting from the x.

When you are translating downward, you are subtracting from the y.

In this case, translate each point 8 units left and 13 units down:

S(0 , 10)

S(0 (- 8) , 10 (- 13)) = S'(-8 , -3)

T(8 , 10)

T(8 (-8) , 10 (-13)) = T'(0 , -3)

U(1 , 5)

U(1 (-8) , 5 (-13)) = U'(-7 , -8)

~

S(-8,-3), T(0, -3), and U(-7, -8)

Step-by-step explanation:

for all of the coordinates, you would subtract 8 from their X-values, and subtract 13 from their Y-values.

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.