Which value of x would make Line segment T V is parallel to Line segment Q S? 3 8 10 11
The correct answer and explanation is:
To determine which value of xx makes the line segment TVTV parallel to the line segment QSQS, we need to understand the relationship between parallel lines and their slopes.
Step 1: Understand the context
- Two line segments are parallel if and only if their slopes are equal.
- So, the slope of TVTV must be equal to the slope of QSQS.
Step 2: Formula for slope
The slope mm between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is: m=y2−y1x2−x1m = \frac{y_2 – y_1}{x_2 – x_1}
Step 3: Identify points and write expressions for slopes
Suppose the coordinates of points TT, VV, QQ, and SS involve xx in some way. Without the exact coordinates, let me give you a generic example:
- Let T=(x1,y1)T = (x_1, y_1)
- Let V=(x2,y2)V = (x_2, y_2)
- Let Q=(x3,y3)Q = (x_3, y_3)
- Let S=(x4,y4)S = (x_4, y_4)
You would set: slope of TV=slope of QS\text{slope of } TV = \text{slope of } QS y2−y1x2−x1=y4−y3x4−x3\frac{y_2 – y_1}{x_2 – x_1} = \frac{y_4 – y_3}{x_4 – x_3}
Step 4: Solve for xx
Using the above equation and plugging in the coordinates with xx in them, solve for xx.
Example:
Suppose the points are:
- T=(3,2x)T = (3, 2x)
- V=(x,8)V = (x, 8)
- Q=(4,6)Q = (4, 6)
- S=(10,14)S = (10, 14)
Slope of TVTV: mTV=8−2xx−3m_{TV} = \frac{8 – 2x}{x – 3}
Slope of QSQS: mQS=14−610−4=86=43m_{QS} = \frac{14 – 6}{10 – 4} = \frac{8}{6} = \frac{4}{3}
Set the slopes equal: 8−2xx−3=43\frac{8 – 2x}{x – 3} = \frac{4}{3}
Cross-multiply: 3(8−2x)=4(x−3)3(8 – 2x) = 4(x – 3) 24−6x=4x−1224 – 6x = 4x – 12
Bring variables to one side: 24+12=4x+6×24 + 12 = 4x + 6x 36=10×36 = 10x x=3610=3.6x = \frac{36}{10} = 3.6
Step 5: Compare with given options
The values you gave are: 3, 8, 10, 11. The calculated x=3.6x = 3.6 is not one of them, so maybe the coordinates or context is different.
Summary:
- To make TV∥QSTV \parallel QS, their slopes must be equal.
- Calculate the slopes of both segments in terms of xx.
- Set the slopes equal.
- Solve for xx.
- Compare with the given options to pick the correct xx.
If you can provide the coordinates or more context about TT, VV, QQ, and SS, I can give you the exact value of xx from your options.