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Assume each figure shown has the same orientation. Which figure is the image of square LMNP after a translation of (x, y) → (x + 5, y – 3)?

Assume each figure shown has the same orientation Which figure is the image of square LMNP after a translation of x y x 5 y 3 class=

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InesWalston

Answer-

Figure 4 is the image of square LMNP after a translation of (x, y) → (x + 5, y – 3)

Solution-

The co-ordinates of the vertices are,

L = (-3, 1)

M = (-1, 1)

N = (-1, -1)

P = (-3, -1)

A translation of (x, y) → (x + 5, y – 3) means, the point must be shifted 5 units right and then 3 units down.

After the transformation the new co-ordinates will be,

L = (-3+5, 1-3) = (2, -2)

M = (-1+5, 1-3) = (4, -2)

N = (-1+5, -1-3) = (4, -4)

P = (-3+5, -1-3) = (2, -4)

These are the co-ordinates of the figure no. 4

You can use the fact that when the figure is origin shifted, then all its coordinates are shifted.

The shifted square LMNP according to given condition would be

4th square

How to draw a shifted figure if the shifts are provided?

Suppose the graph is drawn on the coordinate plane.

Let the shifting be (x,y) → (x+a, y+b)

Then, add 'a' to all x coordinates of the graph's points. Add 'b' to all y coordinates of the graph's points.

The resultant set of new points will be plotted.

How to find the new shifted graph for given graph?

Since the origin shift is (x, y) → (x + 5, y – 3)

(it is called origin shift since we think of it as the origin was picked and placed at the point (3,5)(in this case) and now everything will be measured from this new axis frame)

Thus, the points LMNP will also move. Let we take point M.

Its old coordinates from the graph are deduced as (x = -1, y = 1)

Thus, its new coordinates will be (x+5 = -1+5 =4 , y -3 =1-3=2)

Thus, new coordinate for M will be on (4,2)

Seeing that in graph, we see its the top-right point  of the 4th square. Since origin shift doesn't distort the surface of the graph(as all points just shift with same distance and it can be seen as the graph staying at the same place and origin moving), thus, we conclude that the 4th square will be the shifted graph.

Thus,

The shifted square LMNP according to given condition would be

4th square


Learn more about origin shift of graph in coordinate axis here:

https://brainly.com/question/11901218

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