Imagine you're moving along the segment. Since the midpoint is in the middle of the segment (obviously), it means that when you've traveled from G to A, you're halfway through your journey, along both x and y directions. So, let's break the problem in two and analyze both directions.

Along the x axis, you've moved from -3 to 1, so you moved 4 units forward. This means that you have 4 units still to go, and your journey will end at coordinate 5.

Similarly, along the y axis, you've moved from 5 to -4, so you moved 9 units downward. This means that you have 9 units still to go, and your journey will end at coordinate -13.

So, the coordinates of the endpoint are $T = (5,-13)$

If you prefer a more analyitical approach, simply write the definition of the midpoint and solve it for the coordinates of T.

We have $G = (-3, 5)$ and $T = (x_T,y_T)$ . The midpoint is computed as

$A = \left( \frac{-3+x_T}{2},\frac{5+y_T}{2} \right) = (1, -4)$

So, you have the equations

$\frac{-3+x_T}{2} = 1,\qquad \frac{5+y_T}{2} = -4$

Multply both equations by 2 to get

$-3+x_T = 2,\qquad 5+y_T = -8$

Move the constants to the right hand sides to get

$x_T = 5,\qquad y_T = -13$

8 0

2 years ago

Explain how to create a translation

sukhopar [10]

By translating a shape, you are basically moving it around the graph. For example, one of the points of your shape could be on the origin (0,0). You could then translate it 4 units up and 6 units to the left. You would write this translation as (x-6, y+4). If you were starting at (0,0) your point translation would be at (-6, 4), but if you were to translate a point at (1, 1) your translated point would be at (-5, 5).

7 0

2 years ago

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