Work out the coordinates of the point halfway between the origin and point B. The origin is (0, 0). Point B is at (1, 9). The midpoint formula is: [tex]\( \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \)[/tex] So, the midpoint is [tex]\( \left( \frac{0 + 1}{2}, \frac{0 + 9}{2} \right) = (0.5, 4.5) \)[/tex]
Answer (2)
To find the coordinates of the point halfway between two points, we use the midpoint formula. The midpoint formula is given by:
( 2 x 1 + x 2 , 2 y 1 + y 2 )
In this case, the points we are interested in are the origin ( 0 , 0 ) and point B ( 1 , 9 ) .
Substitute the coordinates into the formula :
For the x-coordinate: x 1 = 0 , x 2 = 1
For the y-coordinate: y 1 = 0 , y 2 = 9
Calculate the midpoint :
The x-coordinate of the midpoint is: 2 x 1 + x 2 = 2 0 + 1 = 0.5
The y-coordinate of the midpoint is: 2 y 1 + y 2 = 2 0 + 9 = 4.5
Write the coordinates of the midpoint :
The coordinates of the midpoint are ( 0.5 , 4.5 ) .
This solution confirms that the point halfway between the origin ( 0 , 0 ) and point B ( 1 , 9 ) is indeed ( 0.5 , 4.5 ) . This point is equidistant from both the origin and point B on the Cartesian plane.
The coordinates of the point halfway between the origin (0, 0) and point B (1, 9) are (0.5, 4.5). This is found using the midpoint formula. By substituting the coordinates into the formula, we arrive at the midpoint's coordinates.
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