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13 days ago

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

Mathematics

2 answers:

AnnZ [3.8K]13 days ago

6 0

Answer: The coordinates of point T are (13, -6).

Step-by-step explanation: Given that point S is the midpoint of segment RT, with coordinates R(-9, 4) and S(2, -1),

we need to determine the coordinates of point T.

The midpoint formula states that the midpoint between points (a, b) and (c, d) is ((a + c)/2, (b + d)/2).

Let T be (h, k). According to the problem:

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

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

Solving these equations yields T at (13, -6).

So, the required coordinates for point T are (13, -6).

tester [3.9K]13 days ago

3 0

Point T has the coordinates (13, -6).

Detailed explanation

Given Information:

Point S(2, -1) is the midpoint of segment RT.
Point R is located at (-9, 4).

Goal:

Determine the coordinates of endpoint T.

Method:

A midpoint coordinates represent the point exactly halfway between two endpoints on a segment.

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

This formula calculates the midpoint's x and y by averaging the x and y of both endpoints (x₁, y₁) and (x₂, y₂).

The midpoint is given as M = S(2, -1).
Define R(x₁, y₁) = (-9, 4) and find T(x₂, y₂).

We proceed to find T’s missing coordinates.

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

Thus, part 1 involves computing the x-coordinate of T, and part 2 the y-coordinate.

Part 1

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

Multiply both sides by 2.

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

Add 9 to both sides to isolate T's x-coordinate.

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

Part 2

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

Multiply both sides by 2.

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

Subtract 4 from both sides to solve for T's y-coordinate.

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

Hence, the coordinates of point T are (13, -6).

Additional resources

How to find the equation of a line in slope-intercept form parallel to a given line and passing through a specific point: brainly.com/question/1473992
Another example of midpoint calculation: brainly.com/question/3269852
Determining the equation of Nolan’s line: brainly.com/question/2657284

Keywords: midpoint, missing endpoint, line segment, endpoints, middle, between, average, abscissa, ordinate, coordinates, R, S, T

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