9. triangle xyz with vertices x(-3, 7), y(-2, 1), and z(-5,2:
(a) reflection: in the x-axis
(b)translations: (x, y) —> (x + 9, y + 2)

x’
y’
z’

X'(6,-5)

Y'(7,1)

Z'(4,0)

Step-by-step explanation:

First, the reflection across the x-axis. The rule for reflection across the x-axis is:

(x,y) -> (x,-y)

Next the translation. This is easy, simply add 9 to all x values, and 2 to all y values.

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form