there are several possible heights at which the higher end of the bridge can be attached to the higher mountain

answer : the point moved thirteen places to the right

on the number line, a point is moved from -8 to 5

on a number line, negative numbers on the left side of 0   and positive numbers on the right side of 0.

to move from -8 to 5 , we move to the left

start from -8 , move to -7 then -6 then -5 then -4 then -3 then -2 then -1 then 0 then 1 then 2 then 3 then 4 and finally 5

so we moved 13 placed to the right.

the point moved thirteen places to the right

step-by-step explanation:

the line y=x is the line where the x and y coordinates of each point, are equal.

so this line is the line through the origin (0, 0), which makes an angle of 45° with the x-axis.

we draw triangle abc. to reflect this triangle with respect to the line y=x, we draw perpendiculars from the points a, b and c to to line y=x, and extend the perpendiculars so that the lint y=x is a perpendicular bisector of these line segments. 

we see that a(5, 3) is mapped to a'(3, 5)

and all the other points p(a, b) of the original triangle are mapped to p'(b,a)

the last statement is true for each point x and its reflection x', also it is true that the line y=x is the perpendicular bisector of xx' and yy'.

to prove these, check the second picture.

let the coordinates of x be (a, b), we want to find the coordinates of its reflection point with respect to the line y=x, point x'.

let m be the point on the line y=x, such that xm=mx'

let n be the point (b, b) which surely is on the line.

now, x'm=mx, nm is common and m(x'mn)=m(xmn)=90°, so by side-angle-side congruence postulate, the triangles x'mn and xmn

  are congruent, so nx=nx'

clearly the x coordinate of x' is b, so the y coordinate of x' is 

b+nx'=b+nx=a

so the coordinates of x' are (b, a)

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