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Answer:
The answer is below
Step-by-step explanation:
Two triangles are said to be similar if their corresponding angles are equal and the corresponding sides are in proportion.
The distance between two points on the coordinate plane is given as:
In triangle STU:
|QR| / |TU| = 4/2 = 2
|PR| / |SU| = 6/3 = 2
|PQ| / |ST| = 2√13 / √13 = 2
Hence:
|QR| / |TU| = |PR| / |SU| = |PQ| / |ST|
Therefore, △PQR and △STU are similar triangles since the ratio of their sides are in the same proportion.
The equation 
is plotted on graph below (red line)
Translating
three units to the left can be done by choosing any coordinates on .
Let choose (0,0) and (2,1)
Translating 3 units on to the left gives the new coordinates (0-3, 0)=(-3,0) and (2-3, 1)=(-1, 1)
The gradient of the two functions will stay the same since the lines are parallel to each other, so m = 0.5
By joining the two coordinates (-3,0) and (-1,1), we see that the translated line crosses y-axis at 1.5
The equation of translated line is given
Translating
Let choose (0,0) and (2,1)
Translating 3 units on to the left gives the new coordinates (0-3, 0)=(-3,0) and (2-3, 1)=(-1, 1)
The gradient of the two functions will stay the same since the lines are parallel to each other, so m = 0.5
By joining the two coordinates (-3,0) and (-1,1), we see that the translated line crosses y-axis at 1.5
The equation of translated line is given