Find the distance between (3,4) and (4,-3)

Question

(A) 5√2

(B) 7

(C) √2

(D) 7√2

(E) None of the above

For this I got; (A) 5√2. Is this correct?

Answer 1

(3,4) and (4, -3)

d = square root{ (3 - 4)^2 + ( 4 - -3)^2}

d= square root { (-1)^2 + 7^2}

d= square root ( 1 + 49)

d = square root (50) = 5 square root of 2

You are correct! Congrats : )

Answer 2

You could use the distance formula and calculate the exact number

Or just plot the two points and notice that the y coordinates are 7 apart, and the distance is slightly greater than 7, as you could form a right triangle and the distance is the hypotenuse which is slightly larger than the vertical side of the triangle.

The only answer slightly larger than 7 is A, 5 sqr 2 = about 5 x 1.414 = 7.07 or slightly larger than 7

B and C are incorrect. D is a little too large.

You might use this method on a time pressure test, to avoid doing unnecessary calculations. Or just to check your answers