Plot the following co-ordinates and find the fourth point D to make a square A (-1,3) B (1,-1) C(5,1). Once you have found the missing coordinate use pythagoras to calculate the length of the sides.

1) The fourth point 'D' to make a square is D(3, 5)

2) The length of the side of the square is 2·√5 units

Step-by-step explanation:

1) The coordinates to be plotted are;

A(-1, 3), B(1, -1), C(5, 1)

Using Microsoft Word, the given points are plotted and the point D is found by noting that the sides BC and AD of the square are parallel and equal in length and the point 'C' is 4 units to the right and 2 units upwards, from the point 'B', therefore, the point 'D' will be located at 4 units to the right and 2 units upwards, from the point 'A' which has coordinates of D(3, 5)

The fourth point 'D' to make a square is D(3, 5)

2) Using Pythagoras's theorem, the length of a side of the square (AB) is given as follows;

AB = √((3 - (-1))² + (1 - (-1))²) = √20 = 2·√5

The length of the side of the square, AB = BC = CD = AD = 2·√5

the value of x is 9 ⇒ answer b

step-by-step explanation:

* we can solve this problem using cosine and sine rule

- in δ abc

∵ ab = 36 , bc = 28 , ac = 16

- lets find the measure of angle b using the cosine rule

∵ cos b = [ab² + bc² - ac²]/2(ab)(bc)

∴ cos b = [36² + 28² - 16²]/2(36)(28)

∴ cos b = 19/21

∴ m∠b = cos^-1(19/21) ≅ 25°

- lets find the measure of angle a using the sine rule

∵ sina/bc = sinb/ac = sinc/ab

∴ sina/28 = sin25°/16 ⇒ by using cross multiplication

∴ sina = 28 × sin25°/16

∴ sina = 0.7396

∴ m∠a = sin^-1(0.7396) ≅ 48°

- from the figure m∠abd = m∠dbc

∵ m∠abc = 25°

∴ m∠abd = 25°/2 = 12.5°

- in δabd

∵ m∠a = 48° , m∠abd = 12.5°

∵ the sum of the measures of the interior angles of any δ is 180°

∴ m∠adb = 180° - (48° + 12.5°) = 119.5°

∵ ab = 36

∵ ad = x

- use the sine rule to find x

∵ sin∠adb/ab = sin∠abd/x

∴ sin119.5°/36 = sin12.5°/x ⇒ by using cross multiplication

∴ x = 36 × sin12.5°/sin119.5° = 8.95 ≅ 9

* the value of x is 9