Find the coordinates of M' after a reflection of the triangle across the parallel lines; first across the line y = -3 and then across y = 2. Answer in (a, b) form. Part 9a

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Explanation:

The first step is to locate point M. It is at (-3, -5). Ignore the other points as your teacher is not asking to transform them.

Reflecting point M over the line y = -3 will have us move 2 units up to arrive at the line of reflection, and then we move 2 more additional units up to get to N = (-3, -1).

Now reflecting point N over the line y = 2 will have us move (-3,-1) three units up to get to the line of reflection, and then we move up another 3 units to get to P = (-3,2) which is the last stop. This is also the location of point M'.

See diagram below.

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Extra info: Overall, those two reflections combine to a translation of shifting 10 units up. Algebraically, we can write the translation rule . Two reflections only turn into a translation if and only if the lines of reflection are parallel.

Perimeter == 10 + 4√10

Step-by-step explanation:

Let the length of the smaller leg be x and thus since the bigger leg is 3 times the size of the smaller one, the bigger leg is 3x.

Now, from the question we are given that the hypotenuse is 10 inches.

Now since this is a right angle triangle, let's use Pythagoras theorem to which says;

a² + b² = c²

Where c is the hypotenuse, while a and b are the other sides of the triangle.

Thus, fixing x and 3x for a and b respectively and 10 for c, we have;

x² + (3x)² = 10²

So, x² + 9x² = 100

Thus, 10x² = 100

Divide both sides by 10 to get,

x² = 10

Take square root of both sides to get ; x = √10

Thus since one side is x and the other 3x,thus the dimensions of the triangle are √10, 3√10 and 10.

Now, perimeter of triangle is the sum of all 3 sides.

Thus perimeter = (√10) + 3(√10) + 10

= 10 + 4√10