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20 votes
20 votes
P(-9,-4) Q(-7,-1) whats is PQ

User Saurav Dangol
by
2.8k points

1 Answer

18 votes
18 votes

Explanation:

I assume the question is about the distance between both points.

2 points in the coordinate grid create a right-angled triangle :

their direct connection (distance) is the Hypotenuse (the baseline, it is the side opposite of the 90° angle), and the x and y coordinate differences are the legs.

so, we can use Pythagoras to get the distance.

c² = a² + b²

c being the Hypotenuse, a and b being the legs.

so,

distance² = (-9 - -7)² + (-4 - -1)² = (-9 + 7)² + (-4 + 1)² =

= (-2)² + (-3)² = 4 + 9 = 13

distance = sqrt(13) = 3.605551275...

just in case, if you needed the line equation connecting these 2 points, I would assume the slope-intersect form

y = ax + b

"a" being the slope, "b" being the y-intersect (the y-value when x = 0).

the slope is always the ratio (y coordinate difference / x coordinate difference) when going from one point on the line to another.

using the 2 given points

x changes by +2 (from -9 to -7).

y charges by +3 (from -4 to -1).

the slope is

+3/+2 = 3/2

and our equation looks like

y = 3x/2 + b

now we use the coordinates of 1 point, e.g. (-7, -1), to get b

-1 = 3/2 × -7 + b = -21/2 + b

-1 + 21/2 = b

-2/2 + 21/2 = b

19/2 = b

our equation is then

y = 3x/2 + 19/2

or

y = (1/2)×(3x + 19)

User Paradocslover
by
3.1k points