Solved on Sep 21, 2023

Find the coordinates of point $T$ if the midpoint of line $RT$ is $(3,0)$ and the coordinates of $R$ are $(-1,-4)$ .

STEP 1

Assumptions1. The midpoint of line RT is M=(3,0) . The coordinates of point R are (-1,-4)
3. The midpoint of a line segment is the point that divides the line segment into two equal parts. It is calculated by taking the average of the x-coordinates and the y-coordinates of the two endpoints.

STEP 2

The formula to find the midpoint M of a line segment with endpoints R and is $M = \left(\frac{R_x +_x}{2}, \frac{R_y +_y}{2}\right)$

STEP 3

We know the coordinates of M and R, and we can substitute these values into the formula to find the coordinates of.
$M_x = \frac{R_x +_x}{2}$ $M_y = \frac{R_y +_y}{2}$

STEP 4

Substitute the known values into the equations.
$3 = \frac{-1 +_x}{2}$ $0 = \frac{-4 +_y}{2}$

STEP 5

olve the equations for $_x$ and $_y$ .
For $_x$ Multiply both sides of the equation by2 to get rid of the fraction.
$2 \times3 = -1 +_x$ For $_y$ Multiply both sides of the equation by2 to get rid of the fraction.
$2 \times0 = -4 +_y$

STEP 6

implify the equations to find the values of $_x$ and $_y$ .
For $_x$ $6 = -1 +_x$ $_x =6 +1$ $_x =$ For $_y$ $0 = -4 +_y$ $_y =0 +4$ $_y =4$ The coordinates of point are (,4).

Was this helpful?

Find the coordinates of point $T$ if the midpoint of line $RT$ is $(3,0)$ and the coordinates of $R$ are $(-1,-4)$ .

STEP 1

Assumptions1. The midpoint of line RT is M=(3,0) . The coordinates of point R are (-1,-4)
3. The midpoint of a line segment is the point that divides the line segment into two equal parts. It is calculated by taking the average of the x-coordinates and the y-coordinates of the two endpoints.

STEP 2

The formula to find the midpoint M of a line segment with endpoints R and is $M = \left(\frac{R_x +_x}{2}, \frac{R_y +_y}{2}\right)$

STEP 3

We know the coordinates of M and R, and we can substitute these values into the formula to find the coordinates of.
$M_x = \frac{R_x +_x}{2}$ $M_y = \frac{R_y +_y}{2}$

STEP 4

Substitute the known values into the equations.
$3 = \frac{-1 +_x}{2}$ $0 = \frac{-4 +_y}{2}$

STEP 5

olve the equations for $_x$ and $_y$ .
For $_x$ Multiply both sides of the equation by2 to get rid of the fraction.
$2 \times3 = -1 +_x$ For $_y$ Multiply both sides of the equation by2 to get rid of the fraction.
$2 \times0 = -4 +_y$

STEP 6

implify the equations to find the values of $_x$ and $_y$ .
For $_x$ $6 = -1 +_x$ $_x =6 +1$ $_x =$ For $_y$ $0 = -4 +_y$ $_y =0 +4$ $_y =4$ The coordinates of point are (,4).

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the coordinates of point TTT if the midpoint of line RTRTRT is (3,0)(3,0)(3,0) and the coordinates of RRR are (−1,−4)(-1,-4)(−1,−4).

STEP 1

Assumptions1. The midpoint of line RT is M=(3,0) . The coordinates of point R are (-1,-4)3. The midpoint of a line segment is the point that divides the line segment into two equal parts. It is calculated by taking the average of the x-coordinates and the y-coordinates of the two endpoints.

STEP 2

The formula to find the midpoint M of a line segment with endpoints R and isM=(Rx+x2,Ry+y2)M = \left(\frac{R_x +_x}{2}, \frac{R_y +_y}{2}\right)M=(2Rx​+x​​,2Ry​+y​​)

STEP 3

We know the coordinates of M and R, and we can substitute these values into the formula to find the coordinates of.Mx=Rx+x2M_x = \frac{R_x +_x}{2}Mx​=2Rx​+x​​My=Ry+y2M_y = \frac{R_y +_y}{2}My​=2Ry​+y​​

STEP 4

Substitute the known values into the equations.3=−1+x23 = \frac{-1 +_x}{2}3=2−1+x​​0=−4+y20 = \frac{-4 +_y}{2}0=2−4+y​​

STEP 5

olve the equations for x_xx​ and y_yy​.For x_xx​Multiply both sides of the equation by2 to get rid of the fraction.2×3=−1+x2 \times3 = -1 +_x2×3=−1+x​For y_yy​Multiply both sides of the equation by2 to get rid of the fraction.2×0=−4+y2 \times0 = -4 +_y2×0=−4+y​

STEP 6

implify the equations to find the values of x_xx​ and y_yy​.For x_xx​6=−1+x6 = -1 +_x6=−1+x​x=6+1_x =6 +1x​=6+1x=_x =x​=For y_yy​0=−4+y0 = -4 +_y0=−4+y​y=0+4_y =0 +4y​=0+4y=4_y =4y​=4The coordinates of point are (,4).

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the coordinates of point $T$ if the midpoint of line $RT$ is $(3,0)$ and the coordinates of $R$ are $(-1,-4)$ .

Assumptions1. The midpoint of line RT is M=(3,0) . The coordinates of point R are (-1,-4)
3. The midpoint of a line segment is the point that divides the line segment into two equal parts. It is calculated by taking the average of the x-coordinates and the y-coordinates of the two endpoints.

The formula to find the midpoint M of a line segment with endpoints R and is $M = \left(\frac{R_x +_x}{2}, \frac{R_y +_y}{2}\right)$

We know the coordinates of M and R, and we can substitute these values into the formula to find the coordinates of.
$M_x = \frac{R_x +_x}{2}$ $M_y = \frac{R_y +_y}{2}$

Substitute the known values into the equations.
$3 = \frac{-1 +_x}{2}$ $0 = \frac{-4 +_y}{2}$

olve the equations for $_x$ and $_y$ .
For $_x$ Multiply both sides of the equation by2 to get rid of the fraction.
$2 \times3 = -1 +_x$ For $_y$ Multiply both sides of the equation by2 to get rid of the fraction.
$2 \times0 = -4 +_y$

implify the equations to find the values of $_x$ and $_y$ .
For $_x$ $6 = -1 +_x$ $_x =6 +1$ $_x =$ For $_y$ $0 = -4 +_y$ $_y =0 +4$ $_y =4$ The coordinates of point are (,4).