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2 votes
Find the distance between the points A (4,6) and B (3,-4)​

User Georgepiva
by
4.7k points

2 Answers

3 votes

Explanation:

right.

to give a little bit more explanation :

we are using actually the Pythagoras formula for right-angled triangles

c² = a² + b²

with c being the Hypotenuse = the opposite side of the 90 degree angle.

now imagine 2 points in a grid of coordinates.

to go from point 1 to point 2 you go for example first a certain distance parallel to the x-axis, and then another distance parallel to the y-axis.

as you can see, you build that way a right-angled triangle, with the direct connection from point 1 to point 2 being the Hypotenuse.

so the direct distance (c) between A and B is then using the Pythagoras formula based on the coordination unit changes we have to make in x and y direction.

A is at coordinates (4,6). Ax = 4, Ay = 6

B is at coordinates (3,-4). Bx = 3, By = -4

so, going from A to B, the distance in x-direction is the difference between 4 and 3 (= 1), and the distance in y- direction is the difference between 6 and -4 (= 10).

since all values are squared first in that formula, it does not matter, if we calculate for example 4-3 or 3-4. but it is important to always only calculate x with x and y with y.

so, c² = 1² + 10² or -1² + (-10)² = 101

and c = sqrt (101) as the other answer calculated already correctly.

User Mgiagnoni
by
4.6k points
5 votes

Answer:

10.05 units

Explanation:

Distance between (A, B)


= \sqrt{ {(3 - 4)}^(2) + {( - 4 - 6)}^(2) } \\ = \sqrt{ {( - 1)}^(2) + {( - 10)}^(2) } \\ = √(1 + 100) \\ = √(101) \\ = 10.0498756 \\ \approx \: 10.05 \: units

User Joachim Birche
by
4.4k points