Find the coordinates of the four points which have integer coordinates and are a distance of root 5 from the point (1, 2). Hint 5=1^2 + 2^2
Step1: Mark the point (1,2) on a Cartesian plane.
Step2: Go 2 units up and 1 unit right that will be your point A (2,4)
Step3: Go 2 units up and 1 unit left that will be your point B (0,4)
Step4: Go 2 units down and 1 unit right that will be your point C (2,0)
Step5: Go 2 units down and 1 unit left that will be your point D (0,0)
please hwo does this work i need the woring out to understnad
so, move left-right 1 and up-down 2
or left-right 2 and up-down 1.
One such point will be (1+1,2+2) = (2,4)
I think you will find 8 such points, not 4.
These are your four points
A: (2,4)
B: (0,4)
C: (2,0)
D: (0,0)
Hope this helps
hey maybe if you think about it like sqrt= square root
\sqrt{5}=\sqrt{1^2+2^2}
move one left or right
move 2 up or down
hey
To find the coordinates of the four points that are a distance of √5 from (1, 2) and have integer coordinates, we can use the distance formula. The distance formula is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, (x1, y1) = (1, 2). Let's substitute this into the formula:
√5 = √((x2 - 1)^2 + (y2 - 2)^2)
To find all the integer coordinates that satisfy this equation, we need to consider the possible values of (x2 - 1) and (y2 - 2) that satisfy the equation:
(x2 - 1)^2 + (y2 - 2)^2 = 5
Since 5 = 1^2 + 2^2, the equation becomes:
(x2 - 1)^2 + (y2 - 2)^2 = 1^2 + 2^2
Expanding this equation, we get:
x2^2 - 2x2 + 1 + y2^2 - 4y2 + 4 = 1 + 4
Simplifying further:
x2^2 - 2x2 + y2^2 - 4y2 = 0
Now let's try to find the integer solutions for this equation. By trying out different integer values for (x2 - 1) and (y2 - 2), we can find the corresponding values for x2 and y2.
Let's consider some possible values:
Case 1: (x2 - 1) = 0 and (y2 - 2) = 0
In this case, x2 = 1 and y2 = 2. So one of the points is (1, 2).
Case 2: (x2 - 1) = 1 and (y2 - 2) = 1
In this case, x2 = 2 and y2 = 3. So another point is (2, 3).
Case 3: (x2 - 1) = -1 and (y2 - 2) = 1
In this case, x2 = 0 and y2 = 3. So another point is (0, 3).
Case 4: (x2 - 1) = 1 and (y2 - 2) = -1
In this case, x2 = 2 and y2 = 1. So another point is (2, 1).
Therefore, the four points that have integer coordinates and are a distance of √5 from (1, 2) are:
(1, 2), (2, 3), (0, 3), and (2, 1).