Question 80

Point P is the midpoint of seg AB. Coordinates of P are (1,1) and A are (4,3). What are the coordinates of point B?

Solution

Coordinates of mid point of line joining A $$(x_1,y_1)$$ and B $$(x_2,y_2)$$ = $$(\frac{x_1 + x_2}{2} , \frac{y_1 + y_2}{2})$$

Let coordinates of B $$(x , y)$$

A = (4,3) and P = (1,1)

=> $$1 = \frac{4 + x}{2}$$

=> $$x = 2 - 4 = -2$$

Similarly, $$1 = \frac{3 + y}{2}$$

=> $$y = 2 - 3 = -1$$

Thus, coordinates of B (-2,-1)

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Point P is the midpoint of seg AB. Coordinates of P are (­1,1) and A are (4,3). What are the coordinates of point B?