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A line segment has endpoints at (–4, –6) and (–6, 4). Which reflection will produce an image with endpoints at (4, –6) and (6, 4)?
a reflection of the line segment across the x-axis
a reflection of the line segment across the y-axis
a reflection of the line segment across the line y = x
a reflection of the line segment across the line y = –x
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a reflection of the line segment across the y-axis

Explanation:

The transformations of the end points are:

       Preimage         Image

(–4, –6)     →    (4, –6) (–6, 4)       →    (–6, 4)

The means that, for every end point, the x-coordinate changes the sign and the y-coordinate remains unchanged.

That rule is:

(x, y) → (- x, y): this is a reflection across the y-axis.

Keeping the y-coordinate and changing the sign of the x-coordinate is a reflection across the y -axis. It is like a mirror image, where the mirror is placed along the y-axis. The figure keeps the same distance from the y-axis (the mirror) but changes sides, which is represented by the change of x to - x,  while the altitude (the y-coordinate) keeps unchanged.

In a right-angled triangle: 1- the hypotenuse is the longest side2- we can apply pythagorean rule which states that: (hypotenuse)^2 = (side1)^2 + (side2)^2for the given triangle,longest side is 15 cm  side1 = 9 cmside2 is 12 cm  to check whether the triangle is right-angled or not,compare (15)^2 to the summation of (9)^2 and (12)^in other words, compare 225 to the summation of 81 and 144if they are both equal, then the triangle is right-angles, otherwise, it is not.you haven't provided the diagram showing her work, so i cannot tell the choice. however, apply my explanation to the question you have.

Answer (b) they're often rural migrants with no title to housing or rights to established businesses