posted by .

Find the distance from the point (5, 6) to the line x + y = 3

I don't get the x+y=3 mean

Well, it means the shortest distance, that along a perpendicular from the point to the line.

slope of the line y = -x + 3 is -1
so
the slope of the perpendicular is -1/-1 = 1

then find the equation of that perpendicular through the given point
y = 1 x + b
goes through our point (5,6)
so
6 = 5 + b
b = 1
so the equation of our perpendicular is
y = x + 1

Now where does that hit our original line?
y = -x + 3
y = x + 1
2 y = 4
y = 2
then x = 1
so at
(1,2)
NOW I have an easy problem that I bet you know how to do.
Find the distance from
(5,6) to (1,2)

d^2 = (1-5)^2 + (2-6)^2
d^2 = 16 + 16
d^2 = 2*4^2
d = 4 sqrt 2

If (a,b) is a point not on the line
Ax + By + C = 0
then the shortest distance from the point to the line is
|aA + bB + C|/√(A^2+b^2)

shortest distance
= |5(1) + 6(1) -3|/√(1^2+1^2)
= 8/√2
which rationalizes to 4√2

Are they supposed to know that Reiny ?

not sure about grade 9, but I just checked an old grade 10 text from Ontario, and I used to teach it in 10
The proof followed your method using a general case.

I think you had best learn that recipe Lily.

## Similar Questions

1. ### calc

standard equation of circle concentric with X^2+Y^2-2X-8Y+1=0 and tangent to line 2X-Y=3 Complete the squares to find the center of the circle. X^2+Y^2-2X-8Y+1=0 (x-1)^2+(y-4)^2 - 16 =0 The center is (1,4) and the radius for the given …
2. ### Math

How do you: Find the shortest distance, to two decimal places from the origin to the line x - 2y = - 8 without using the formula. Finding the shortest distance, to two decimal places, from the point P ( 7,5) to the line 2x+3y = 18?
3. ### Physics

The drawing shows four point charges. The value of q is 2.4 µC, and the distance d is 0.86 m. Find the total potential at the location P. Assume that the potential of a point charge is zero at infinity. This is a question of electric …
4. ### Physics repost

Posted by Mary on Monday, September 3, 2007 at 7:11pm. download mp3 free instrumental remix The drawing shows four point charges. The value of q is 2.4 µC, and the distance d is 0.86 m. Find the total potential at the location P. …
5. ### calculus

Consider line segments which are tangent to a point on the right half (x>0) of the curve y = x^2 + 1 and connect the tangent point to the x-axis. If the tangent point is close to the y-axis, the line segment is long. If the tangent …
6. ### Math

I have a series of questions that I did. They lead up to the last question I can't solve. Could you check my math and help me with the last question?
7. ### precalc

I;m not sure if i am doing this right...I keep getting a negative intersection point, which doesn't seem possible. Please help! a) find the equatoin of line 1 which passes through (1,3) and (9,7) I get y=3+1/2(x+1)or y=1/2x+2.5 b) …
8. ### geometry

a point F is at a certain distance from a line AB .Another point P is moving in a plane such that the ratio of it's distance from F and line AB remains constant .find the locus of the point P
9. ### Math

For the given point and line, find by projection the point on the line that is closest to the given point and use perp to find the distance from the point to the line. P (3,-5) line: x = (2,-4)+t(3,-4)
10. ### Math

A line 'l' intersects line 'm' at point A at 45 degree angle. B and C are points on line m, where the distance from B to A is equal to the distance from A to C. How many points on line 'l' are equidistant from points B and C?

More Similar Questions