The figure shows triangle abc and some of its transformed images on a coordinate grid: a coordinate plane is shown. triangle abc is formed by the points 2 comma 5, 2 comma 3 and 4 comma 3. triangle 2 is formed by the points negative 3 comma 5, negative 3 comma 3, and negative1 comma 3. triangle 1 is formed by the points negative 4 comma 5, negative 4 comma 3, and negative 6 comma 3. triangle 3 is formed by the points negative 6 comma 2, negative 4 comma 2, and negative 4 comma 0. triangle 4 is formed by the points 2 comma negative 1, 4 comma negative 1 and 4 comma negative 3. which of the four triangles was formed by a translation of triangle abc? 1 2 3 4

your answer is 2nd triangle.

let me start with the meaning of term translation.

translation means moving a figure on the same plane by changing   some amount of x coordinate   and some amount of y coordinate in all the vertices of that figure.the value of change is integral value. suppose i am translating a triangle so if i can add or subtract some integral value to x coordinate(i.e   vertex a) than we have to add or subtract same integer to b and c.applying same procedure for y cordinate.

now come to your question

by applying simple addition and subtraction in the given coordinate of triangle abc i.e if we add some integral values(x and y can be different)   to vertices triangle 2 is the exact translation.

x coordinate of   a= 2 =2-5=-3,   x coordinate of   b=2=2-5=-3, x coordinate of   c=4=4-5=-1, y coordinate of a=5=5-0=5+0, y coordinate of b=3-0=3+0=3, y coordinate of c=3=3-0=3+0

a(2,5),b(2,3),c(4,3) is translated to a(-3,5),b(-3,3),c(-1,3).

none of the other figure satisfies the above criteria. triangle 2 is the correct answer.