Question

Find the missing endpoint if s is the midpoint of rt r(-9,4) and s(2,-1) ; find T

Answer 1

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

$\left(\dfrac{a+c}{2},\dfrac{b+d}{2}\right).$

Let (h, k) be the co-ordinates of point T. Then, according to the given information, we have

$\left(\dfrac{-9+h}{2},\dfrac{4+k}{2}\right)=(2,-1)\\\\\\\Rightarrow \dfrac{-9+h}{2}=2\\\\\Rightarrow -9+h=4\\\\\Rightarrow h=4+9\\\\\Rightarrow h=13$

and

$\dfrac{4+k}{2}=-1\\\\\Rightarrow 4+k=-2\\\\\Rightarrow k=-2-4\\\\\Rightarrow k=-6.$

Thus, the required co-ordinates of point T are (13, -6).

Answer 2

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 $\boxed{\boxed{ \ M = \bigg( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \bigg) \ }}$

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.

$\boxed{ \ (2, -1) = \bigg( \frac{-9 + x_2}{2}, \frac{4 + y_2}{2} \bigg) \ }$

Therefore, we complete part-1 for abscissa of T and part-2 for ordinate of T.

Part-1

$\boxed{ \ \frac{-9 + x_2}{2} = 2 \ }$

Both sides are multiplied by 2.

$\boxed{ \ -9 + x_2 = 4 \ }$

Both sides are added by 9, and we get the abscissa of T.

$\boxed{\boxed{ \ x_2 = 13 \ }}$

Part-2

$\boxed{ \ \frac{4 + y_2}{2} = -1 \ }$

Both sides are multiplied by 2.

$\boxed{ \ 4 + y_2 = -2 \ }$

Both sides are subtracted by 4, and we get the ordinate of T.

$\boxed{\boxed{ \ y_2 = -6\ }}$

Thus, the coordinates of T is (13, -6).

Learn more

1. Finding the equation, in slope-intercept form, of the line that is parallel to the given line and passes through a point brainly.com/question/1473992
2. Another case about the midpoint brainly.com/question/3269852
3. Determine the equation represents Nolan’s line  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