Question

The point P(p,5) lies on the line joining A(1,2) and B(-4,7). What are the coordinates of point P?

A) P(1, 5)
B) P(-4, 5)
C) P(3, 5)
D) P(-1, 5)

Answer 1

The coordinates of point P are P(-2, 5)

Step-by-step explanation:

To find the coordinates of point P, we can use the formula for finding the equation of a line. The equation of the line passing through points A(1,2) and B(-4,7) is:

(y - y1) = (y2 - y1) / (x2 - x1) * (x - x1)

Substituting the values, we get:

(y - 2) = (7 - 2) / (-4 - 1) * (x - 1)

(y - 2) = (-5/5) * (x - 1)

(y - 2) = -1 * (x - 1)

y - 2 = -x + 1

y = -x + 3

Now, substituting the value of y as 5, we can solve for x:

5 = -x + 3

x = -2

So the coordinates of point P are P(-2, 5), which is option D.