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kirza4 [7]
4 years ago
13

Write an equation in point-slope form for each line (If possible please show work)

Mathematics
1 answer:
Archy [21]4 years ago
8 0

Answer: y-2=1/4(x-1)

Step-by-step explanation:

The formula for point-slope is y-y₁=m(x-x₁). Since we are given the slope m, we can fill that in. We are also given the point (x₁,y₁). We can also fill that in.

y-2=1/4(x-1)

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XYZ has coordinates X(2, 3), Y(1,4), and Z(8,9). A translation maps X to X'(4,7). What are the coordinates for Y' and Z' for thi
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Answer:

The coordinates are Y'(x,y) = (3, 8) and Z'(x,y) = (10, 13).

Step-by-step explanation:

First, we have to derive an expression for translation under the assumption that each point of XYZ experiments the same translation. Vectorially speaking, translation from X to X' is defined by:

X'(x,y) = X(x,y) + T(x,y) (1)

Where T(x,y) is the vector translation.

If we know that X(x,y) = (2,3) and X'(x,y) = (4,7), then the vector translation is:

T(x,y) = X'(x,y)-X(x,y)

T(x,y) = (4,7) - (2,3)

T(x,y) = (2, 4)

Then, we determine the coordinates for Y' and Z':

Y'(x,y) = Y(x,y) + T(x,y)

Y'(x,y) = (1,4) + (2,4)

Y'(x,y) = (3, 8)

Z'(x,y) = Z(x,y) + T(x,y)

Z'(x,y) =(8,9) + (2,4)

Z'(x,y) = (10, 13)

The coordinates are Y'(x,y) = (3, 8) and Z'(x,y) = (10, 13).

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