Point S is on line segment \overline{RT}. Given
and
, determine the length \overline{ST}.
The Correct Answer and Explanation is:
To determine the length of segment ST‾\overline{ST}ST, we need to use the distance formula, since we are given the coordinates of points SSS and TTT.
The distance formula is: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}d=(x2−x1)2+(y2−y1)2
Where (x1,y1)(x_1, y_1)(x1,y1) and (x2,y2)(x_2, y_2)(x2,y2) are the coordinates of points SSS and TTT respectively.
Let’s assume the coordinates of SSS are (xS,yS)(x_S, y_S)(xS,yS) and those of TTT are (xT,yT)(x_T, y_T)(xT,yT). If you have the coordinates of SSS and TTT, substitute them into the formula.
For example, if the coordinates of SSS are (4.3,−2.2)(4.3, -2.2)(4.3,−2.2) and the coordinates of TTT are (−8.5,−2.2)(-8.5, -2.2)(−8.5,−2.2), the calculation would be as follows:
- Subtract the x-values: xT−xS=−8.5−4.3=−12.8x_T – x_S = -8.5 – 4.3 = -12.8xT−xS=−8.5−4.3=−12.8
- Subtract the y-values: yT−yS=−2.2−(−2.2)=0y_T – y_S = -2.2 – (-2.2) = 0yT−yS=−2.2−(−2.2)=0
- Square the differences: (−12.8)2=163.84,02=0(-12.8)^2 = 163.84, \quad 0^2 = 0(−12.8)2=163.84,02=0
- Add the squares: 163.84+0=163.84163.84 + 0 = 163.84163.84+0=163.84
- Take the square root: 163.84≈12.8\sqrt{163.84} \approx 12.8163.84≈12.8
Therefore, the length of ST‾\overline{ST}ST is approximately 12.8 units.
This method works whenever you are given the coordinates of two points and want to calculate the distance between them. The important part is to correctly apply the formula and be careful with the signs when subtracting the coordinates.
