Calculate the lengths of the straight lines joining the following pairs of points, leaving your answers in surd form:
(a) A(1,-5), B(6,10);
(b) A(4,-3), B(7,6).
Just use your formula
Dist = √(x2-x1)^2 + (y2-y1)^2 )
= √( 6-1)^2 + (10-(-5))^2 )
= √(25 + 225)
= √ 250) = √25 * √10
= 5√10
Do the 2nd one in the same way
To calculate the lengths of the straight lines joining the given pairs of points, we can use the distance formula, which is derived from the Pythagorean theorem. The formula is:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
(a) For points A(1,-5) and B(6,10):
We can substitute the values into the distance formula:
Distance = √((6 - 1)^2 + (10 - (-5))^2)
Simplifying:
Distance = √(5^2 + 15^2)
Distance = √(25 + 225)
Distance = √250
Therefore, the length of the straight line joining points A and B is √250 in surd form.
(b) For points A(4,-3) and B(7,6):
We can substitute the values into the distance formula:
Distance = √((7 - 4)^2 + (6 - (-3))^2)
Simplifying:
Distance = √(3^2 + 9^2)
Distance = √(9 + 81)
Distance = √90
Therefore, the length of the straight line joining points A and B is √90 in surd form.