The three co-ordinates of a rectangle are A(3,-4), B(-1,4), C(4,2).Find the fourth co-ordinate

#Plz guyz may you help me out this question

The rectangle is slanted with respect to the axes.

Make a sketch to see if the corners are in order.
You can use the graphing tool desmos.com to help you plot.

From the plot, it looks like the three points A, B and C do not form any right-angle, so there must be a typo with the coordinates.

Please check the information provided.

find two perpendicular lines from the three points by finding the slopes between the three pairs

... that is one corner
... you are looking for the opposite corner
... use the slopes from the ends of the sides to find the missing point

this should be very simple by using graph paper

i use the graph paper but i did not make it

Sure, I'd be happy to help you with this question!

To find the fourth coordinate of the rectangle, we can use the fact that a rectangle is a quadrilateral with four right angles. This means that the opposite sides of the rectangle are parallel and equal in length.

To find the fourth coordinate, let's consider the points A(3, -4), B(-1, 4), and C(4, 2). We can start by finding the length of the sides AB, BC, and AC.

Using the distance formula, the distance between two points (x1, y1) and (x2, y2) is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

1. AB:
Using the points A(3, -4) and B(-1, 4):
dAB = sqrt((-1 - 3)^2 + (4 - (-4))^2)
= sqrt((-4)^2 + (4 + 4)^2)
= sqrt(16 + 64)
= sqrt(80)
= 4 * sqrt(5)

2. BC:
Using the points B(-1, 4) and C(4, 2):
dBC = sqrt((4 - (-1))^2 + (2 - 4)^2)
= sqrt((4 + 1)^2 + (-2)^2)
= sqrt((5)^2 + 4)
= sqrt(25 + 4)
= sqrt(29)

3. AC:
Using the points A(3, -4) and C(4, 2):
dAC = sqrt((4 - 3)^2 + (2 - (-4))^2)
= sqrt((4 - 3)^2 + (2 + 4)^2)
= sqrt((1)^2 + (6)^2)
= sqrt(1 + 36)
= sqrt(37)

Since opposite sides of a rectangle are parallel and equal in length, we can conclude that AB is equal in length to the diagonal BD (where D is the fourth coordinate), and BC is equal in length to the diagonal CD. So, we can set up the following equations:

4 * sqrt(5) = sqrt(37)
sqrt(29) = sqrt(37)

Squaring both sides of the equations to eliminate the square roots:
(4 * sqrt(5))^2 = (sqrt(37))^2
(4 * sqrt(5))^2 = 37
(4^2) * (sqrt(5))^2 = 37
16 * 5 = 37
80 = 37 (not true)

(sqrt(29))^2 = (sqrt(37))^2
29 = 37 (not true)

Since none of the equations are true, it means that the given points A(3, -4), B(-1, 4), and C(4, 2) do not form a rectangle. Therefore, we cannot determine the fourth coordinate.