Calculate the lengths of the straight lines joining the following pairs of points, leaving your answers in surd form:
(a) A(4,-3), B(7,6).
What marriage
To calculate the length of the straight line joining two points, say A(x1, y1) and B(x2, y2), we use the distance formula which states that the distance between two points is given by:
d = √[(x2 - x1)² + (y2 - y1)²]
Let's calculate the length of the straight line joining points A(4, -3) and B(7, 6).
Using the distance formula, we have:
d = √[(7 - 4)² + (6 - (-3))²]
= √[3² + 9²]
= √[9 + 81]
= √90
So, the length of the straight line joining points A(4, -3) and B(7, 6) is √90.
change in y = 6 - (-3) = 9
change in x = 7 -4 = 3
so d = sqrt (81 + 9) = sqrt (90)
= 3 sqrt 10