Question

Let PS be the median of the triangle with vertices P(2,2),Q(6,−1) and R(7,3). The equation of line passing through (1,−1) and parallel to PS is _____

Answer 1

The equation of a line that passes through (1, -1) and is parallel to the median PS of the given triangle is y + 1 = -2/9(x - 1). This line has the same slope as PS, which is -2/9.

Step-by-step explanation:

To find the equation of this line, we first need to determine the slope of the median PS. Since PS is a median, it passes through the midpoint of QR.

We can calculate the midpoint of QR by averaging the x and y coordinates of Q and R. This gives us the point (½(6+7), ½(-1+3)) = (6.5, 1).

The slope of PS is then (1 - 2)/(6.5 - 2) = -1/4.5.

The slope of the line parallel to PS must be the same, and hence our line has a slope of -1/4.5 or -2/9.

To write the equation of the line through (1, -1) with a slope of -2/9, we use the point-slope form of a line equation: y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is the point through which the line passes.

Substituting the given point and slope: y - (-1) = -2/9(x - 1).

Simplifying, we get the equation of the line: y + 1 = -2/9(x - 1).