Is the line through points P(-7,2) and Q(7,-6) parallel to the line through points R(14,0) and S(7,4). How do you know?(1 point)
To determine if two lines are parallel, we need to compare their slopes.
The slope of the line through points P(-7,2) and Q(7,-6) can be found using the slope formula:
m₁ = (y₂ - y₁) / (x₂ - x₁)
m₁ = (-6 - 2) / (7 - (-7))
m₁ = (-8) / (14)
m₁ = -4/7
The slope of the line through points R(14,0) and S(7,4) can be found using the slope formula:
m₂ = (y₂ - y₁) / (x₂ - x₁)
m₂ = (4 - 0) / (7 - 14)
m₂ = 4 / (-7)
m₂ = -4/7
The slopes of both lines are the same, m₁ = m₂ = -4/7. Therefore, the line through points P(-7,2) and Q(7,-6) is parallel to the line through points R(14,0) and S(7,4).
To determine if the line through points P(-7,2) and Q(7,-6) is parallel to the line through points R(14,0) and S(7,4), we can compare their slopes.
The slope of a line passing through two points (x1, y1) and (x2, y2) can be calculated using the formula: m = (y2 - y1) / (x2 - x1).
For the line passing through P(-7,2) and Q(7,-6), the slope is:
m1 = (-6 - 2) / (7 - (-7))
= (-8) / (7 + 7)
= -8 / 14
= -4 / 7
For the line passing through R(14,0) and S(7,4), the slope is:
m2 = (4 - 0) / (7 - 14)
= 4 / (-7)
= -4 / 7
Comparing the slopes, we see that the slopes for the two lines are the same (-4/7). Therefore, the line through points P(-7,2) and Q(7,-6) is parallel to the line through points R(14,0) and S(7,4).
Hence, we know that the lines are parallel based on the equality of their slopes.
To determine if the line through points P(-7,2) and Q(7,-6) is parallel to the line through points R(14,0) and S(7,4), we can compare the slopes of these two lines.
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
slope = (y2 - y1) / (x2 - x1)
For the line passing through P(-7,2) and Q(7,-6), the slope is:
slope1 = (-6 - 2) / (7 - (-7))
slope1 = -8 / 14
slope1 = -4/7
For the line passing through R(14,0) and S(7,4), the slope is:
slope2 = (4 - 0) / (7 - 14)
slope2 = 4 / -7
slope2 = -4/7
If the slopes of two lines are equal, then they are parallel. In this case, both slope1 and slope2 are -4/7, which means the line through points P(-7,2) and Q(7,-6) is parallel to the line through points R(14,0) and S(7,4).
Therefore, the answer is "Yes, the line through points P(-7,2) and Q(7,-6) is parallel to the line through points R(14,0) and S(7,4)"