help me on this. Find the shortest distance from the point p(-3,6) to the line x=4?

Answer 1

Hi,

The line x = 4 is a vertical line 4 squares to the right of the x axis. The shortest distance from the point (-3,6) to the vertical line x = 4 is the perpendicular distance from (-3,6) to the vertical line x = 4. That is the horizontal distance which is 4 - (-3) or 7 units apart.

So the shortest distance from (-3,6) to x = 4 is 7 units.

I hope this helps!! :-)

Answer 2

The line
x = 4
is the set of points (x, y) such that x =4 and y = anything.
In other words, the set of points (4,y)

The distance^2 between (4,y) and the point (-3,6) is:
= (4 - (-3))^2 + (y - 6)^2
= 7^2 + (y-6)^2
= 49 + y^2 - 12y + 36
= 85 - 12y + y^2

As a function, this takes the minimum when the derivative = 0, or when:
0 = d/dy(85 - 12y + y^2) = 0 -12 + 2y = 2y - 12
so when
y = 6

So the shortest distance is when y = 6, and thus the distance is:
sqrt(85 - 12*6 + 6^2) = sqrt(85 - 72 + 36) = sqrt(49) = 7

7 it is.

Answer 3

The line "x=4" is a vertical line running through the +4 on the x axis. plot the other point (-3,6) and then move horizontally until you reach the line. it should end up being 7 points.

If that made no sense then you could just recognize that in the point (-3,6) the x part is like(-3,0) and the x=4 is like (4,0)
and the distance between -3 and 4 is 7.

Answer 4

The point (-3,6) is situated 4-(-3)=7 from x=4, which is a vertical line.

Answer 5

x=4 is a vertical line. A point with an x coordinate of -3 is
4-(-3)=7 units from it.

Answer 6

7 units.
the horizontal distance would be the shortest since it is just straight across
(-3, 6) to (4, 6)
is a total of 7 units

Answer 7

x = 4 is a vertical line passing thro` (4,6)
Shortest distance is the horizontal distance ,d ,from (-3 , 6) to (4,6).
This is d = 7

Answer 8

as the refernce line is x=4 and x-cordinate of pint is -3,So, distance is 4-(-3)=7

Answer 9

7cm (boxes or units) in diagonal from each point (oh and x is usually point 0.

Answer 10

The answer is 7.6