Question

A line passes through (2,4) and (-2,2).

a)Find the value of y if (6,y) lies on the
plane.
b)Does this line pass through the point of
Does this line intersect with the line
y=-x+3?
d) your answer was yes in b, in which
quadrant did they intersect?​

Answer 1

a) (6;6)

b) Yes

d) The intersection is on the vertical axis.

Explanation:

a) A(2,4)

B (2,2)

Vecto BA (4, 2)

Vecto n (-4,2)

We have:

(2 - 4) x (X - (-2)) + (2 - (-2)) x (Y - 2) = 0

=> -2X + 4Y - 12 = 0

=> Y = X/2 +3

Let's find the value of y if (6,y) lies on the plane:

Put X = 6 => Y = 6

b)

X/2 + 3 = 3 - X

=> X/2 = -X

=> X =0 -> Y = 3

C (0;3)

d) The intersection is on the vertical axis.

I hope my answer will help you.