Line RS passes through points R (5, 3) and S (-1, 0).
Line PQ is parallel to line RS and passes through points P (3, -1) and Q (-2, y).
What are the coordinates of point Q?
+26396 Line RS passes through points R (5, 3) and S (-1, 0).
Line PQ is parallel to line RS and passes through points P (3, -1) and Q (-2, y).
What are the coordinates of point Q ?
Line PQ is parallel to line RS - cross product |(→S−→R)×(→Q−→P)|=0|[(−10)−(53)]×[(−2y)−(3−1)]|=0|(−6−3)×(−5y+1)|=0(−6)⋅(y+1)−(−3)⋅(−5)=0(−6)⋅(y+1)−15=0(−6)⋅(y+1)=15y+1=−156y=−156−1y=−216y=−72y=−3.5→Q=(−2−3.5)
+980 The lines are parralel. This means they have the same gradient.
First we find the gradient of RS.
The formula for gradient is: m = (y{2}-y{1})/(x{2}-x{1}).
y{2}=0, y{1}=3, x{2}=-1, x{1}=5
m=(0−3)(−1−5)
m=(−3)(−6)
m=12
Now we can sub our gradient into the equation for line PQ's gradient.
m = (y{2}-y{1})/(x{2}-x{1})
12=(y+1)(−2−3) (keep in mind the y corresponds to point Q)
12=(y+1)(−5) Now we solve for y.
−5=2×(y+1)
−5=2×y+2
−7=2×y
y=−3.5
We can check this by substituting y into the equation. Does (-3.5 --1)/(-5) = 1/2?
This is our y coordinate for point Q.
So point Q = (-2, -3.5)
Hope this helps :)
+26396 Line RS passes through points R (5, 3) and S (-1, 0).
Line PQ is parallel to line RS and passes through points P (3, -1) and Q (-2, y).
What are the coordinates of point Q ?
Line PQ is parallel to line RS - cross product |(→S−→R)×(→Q−→P)|=0|[(−10)−(53)]×[(−2y)−(3−1)]|=0|(−6−3)×(−5y+1)|=0(−6)⋅(y+1)−(−3)⋅(−5)=0(−6)⋅(y+1)−15=0(−6)⋅(y+1)=15y+1=−156y=−156−1y=−216y=−72y=−3.5→Q=(−2−3.5)
