Respuesta :
The co-ordinates of the other end-point "T" are (-6, -8) in the case that, the midpoint "M" and one endpoint, "U" of TU are M(-1, - 2) and U(4, 4), respectively.
As per the question statement, one endpoint of a line segment TU lies at U(4, 4) and the midpoint of TU is at M(-1, -2).
Here, we have to calculate the co-ordinates of the other end point "T", and for doing so, we have to know the formula to calculate the coordinates of the midpoint of a line segment whose endpoints are known.
Formula for the abscissa of the midpoint point, (xm) = [tex]\frac{x1+x2}{2}[/tex]
and, Formula for the ordinate of the midpoint point, (ym) = [tex]\frac{y1+y2}{2}[/tex]
[Where, the endpoints of the line segment were, (x1, y1) and (x2, y2).]
(x2, y2) and (xm, ym) data is provided in the question statement itself.
Let us assume that the co-ordinates of point T are (x, y). We will use these variables in the above-mentioned formulae, to form individual linear equations of single variables, and solving them distinctly for "x" and "y", we will obtain our desired answer.
[tex]\frac{x+4}{2} =-1\\or, (x+4)=[(-1)*2]\\or, (x+4)=(-2)\\or, x=[(-2)-4]\\or, x=-(2+4)\\or, x=-6\\[/tex]
Similarly,
[tex]\frac{y+4}{2} =-2\\or, (y+4)=[(-2)*2]\\or, (y+4)=(-4)\\or, y=[(-4)-4]\\or, y=-(4+4)\\or, y=-8\\[/tex]
Hence, (x, y) = (-6, -8), i.e.,
The co-ordinates of point T = (-6, -8).
- Coordinates: In coordinate geometry, coordinates are a combination of numbers that determine the location of a point in the quadrant planes.
- Abscissa and Ordinate: In coordinate geometry, the distance of a point from the y-axis, measured parallelly to the x-axis, is called abscissa or x-coordinate of the point while the distance of a point from the x-axis, measured parallelly to the y-axis, is called ordinate or y-coordinate of the point.
To learn more about Coordinate Geometry, click on the link below.
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