Respuesta :
Answer: The required co-ordinates of point T are (13, -6).
Step-by-step explanation: given that S is the midpoint of the line segment RT, where the co-ordinates of point R are (-9, 4) and that of S are (2, -1).
We are to find the co-ordinates of point T.
We know that
the co-ordinates of the mid-point of a line segment with endpoints (a, b) and (c, d) are given by
[tex]\left(\dfrac{a+c}{2},\dfrac{b+d}{2}\right).[/tex]
Let (h, k) be the co-ordinates of point T. Then, according to the given information, we have
[tex]\left(\dfrac{-9+h}{2},\dfrac{4+k}{2}\right)=(2,-1)\\\\\\\Rightarrow \dfrac{-9+h}{2}=2\\\\\Rightarrow -9+h=4\\\\\Rightarrow h=4+9\\\\\Rightarrow h=13[/tex]
and
[tex]\dfrac{4+k}{2}=-1\\\\\Rightarrow 4+k=-2\\\\\Rightarrow k=-2-4\\\\\Rightarrow k=-6.[/tex]
Thus, the required co-ordinates of point T are (13, -6).
The coordinates of point T are (13, -6).
Further explanation
Given:
- The midpoint of RT is S(2, -1).
- The coordinates of point R is (-9, 4).
Problem:
Find the missing endpoint of T.
The Process:
The midpoint is the coordinates of a point that is located right in the middle of a line segment or two endpoints.
The Midpoint Formula [tex]\boxed{\boxed{ \ M = \bigg( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \bigg) \ }}[/tex]
So, abscissa and ordinate of the midpoint are the averages of both endpoints. i.e., (x₁, y₁) and (x₂, y₂).
- In this case, the midpoint is given by M = S(2, -1).
- Let R(x₁, y₁) = R(-9, 4) and we will determine T(x₂, y₂).
Let's calculate the missing endpoint of T.
[tex]\boxed{ \ (2, -1) = \bigg( \frac{-9 + x_2}{2}, \frac{4 + y_2}{2} \bigg) \ }[/tex]
Therefore, we complete part-1 for abscissa of T and part-2 for ordinate of T.
Part-1
[tex]\boxed{ \ \frac{-9 + x_2}{2} = 2 \ }[/tex]
Both sides are multiplied by 2.
[tex]\boxed{ \ -9 + x_2 = 4 \ }[/tex]
Both sides are added by 9, and we get the abscissa of T.
[tex]\boxed{\boxed{ \ x_2 = 13 \ }}[/tex]
Part-2
[tex]\boxed{ \ \frac{4 + y_2}{2} = -1 \ }[/tex]
Both sides are multiplied by 2.
[tex]\boxed{ \ 4 + y_2 = -2 \ }[/tex]
Both sides are subtracted by 4, and we get the ordinate of T.
[tex]\boxed{\boxed{ \ y_2 = -6\ }}[/tex]
Thus, the coordinates of T is (13, -6).
Learn more
- Finding the equation, in slope-intercept form, of the line that is parallel to the given line and passes through a point https://brainly.com/question/1473992
- Another case about the midpoint https://brainly.com/question/3269852
- Determine the equation represents Nolan’s line https://brainly.com/question/2657284
Keywords: the midpoint, the missing endpoint, the line segment, endpoints, in the middle, between, average, abscissa and ordinate, the coordinates , R, S, T
