Question

Angle between two lines

3. The points p(2,3), 8 (-1,1) and R(5,-1) are the
vertices of triangle PBR. Find the altitude of the
triangle PBR drawn from the point 8 (-1,1).
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Answer 1

To find the altitude of triangle PBR drawn from a given point, we need to find the equation of the line perpendicular to one of the sides. In this case, the slope of line PR is found, and then the slope of the altitude is determined by taking the negative reciprocal. The equation of the altitude is y = x - 7.

Step-by-step explanation:

To find the altitude of triangle PBR drawn from the point 8 (-1,1), we first need to find the equation of line PR. The slope of PR can be found using the formula:

m = (y2 - y1) / (x2 - x1)

Substituting the coordinates of P(2,3) and R(5,-1) into the formula, we find that the slope of PR is -1. Therefore, the equation of line PR is:

y - 3 = -1(x - 2)

To find the equation of the altitude, we need to find the slope of the line perpendicular to PR. Since the product of the slopes of perpendicular lines is -1, the slope of the altitude is 1.

Now, substituting the coordinates of point B(8, -1) into the equation of the altitude, we can find the equation of the altitude:

y - (-1) = 1(x - 8)

Simplifying the equation gives the equation of the altitude as y = x - 7. Therefore, the altitude of triangle PBR drawn from the point B(8, -1) is y = x - 7.

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