Two perpendicular lines PQ and QR intersect at (1, -1). If the equation of PQ is x - 2y + 4 = 0, find the equation of QR.
1 answer:
Answer:
2x + y - 1 = 0
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
x - 2y + 4 = 0 ( subtract x + 4 from both sides )
- 2y = - x - 4 ( divide all terms by - 2 )
y = x + 2 ← in slope- intercept form
with slope m =
Given a line with slope m then the slope of a line perpendicular to it is
= -
= -
= - 2 , thus
y = - 2x + c ← is the partial equation of the perpendicular line
To find c substitute (1, - 1) into the partial equation
- 1 = - 2 + c ⇒ c = - 1 + 2 = 1
y = - 2x + 1 ← in slope intercept form
Subtract - 2x + 1 from both sides
2x + y - 1 = 0 ← in general form
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Answer:
Q (-4, -2); 2 units; Q' will be above the x-axis; 2 unites; no; yes, the y coordinates are multiplied by -1; Q' (-4, 2); R' (-2, 2), S' (1, 5), T' (-2, 5);
Step-by-step explanation:
even after a reflection over the x-axis, each points distance from the x-axis will stay the same
the x-coordinates don't change because the distance from the y-axis stays the same
the picture below shows points of Q'R'S'T', just connect the vertices
