Question

Help!!!!!!!!!!! Photo attached

Answer 1

option A : 25

Explanation:

Given :

P = (- 6, 7) , Q = ( 2 , 1 ) , R = ( -1 , -3)

Find the length of PQ ,QR , PR.

Using distance formula to find the lengths.

`distance = \sqrt{(x_2 - x_1 )^2 + (y_ 2- y_1)^2`

`PQ = √((2 -- 6)^2 + (1-7)^2) = √(8^2 + 6^2 ) = √(64 + 36 ) =√(100) = 10\\\\QR = √((2 --1)^2 + (-3-1)^2)= √(3^2 + 4^2) =√(9+ 16) =√(25) = 5\\\\PR = √((-1--6)^2 + (-3 -7)^2) = √(5^2 + 10^2) = √(25 + 100) = √(125)`

Clearly , the triangle satisfies Pythagoras theorem :

Square of larger side = Sum of squares of other sides.

Therefore , PQR is a right triangle,

with base = 5, height 10 and slant height(hypotenuse) =
`√(125)` .

`Area = (1)/(2) * base * height`

`=(1)/(2) * 5* 10\\\\= 5 * 5 \\\\= 25 \ square\ units`