Question

simon plots a cycling route on a map. each unit represents one kilometer.
what is the total length, in kilometers, of the route?
6 kilometers
7 kilometers
8 kilometers
12 kilometers

Explanation:

Step1: Calculate the length of \(AB\)

Points \(A(0, - 2)\) and \(B(0,5)\). Using the distance formula for vertical points \(\vert y_2 - y_1\vert\). Here \(y_1=-2,y_2 = 5\), so \(AB=\vert5-(-2)\vert=\vert5 + 2\vert=7\) units.

Step2: Calculate the length of \(BC\)

Points \(B(0,5)\) and \(C(4,5)\). Using the distance formula for horizontal points \(\vert x_2 - x_1\vert\). Here \(x_1 = 0,x_2=4\), so \(BC=\vert4 - 0\vert=4\) units.

Step3: Calculate the total length

The total length of the route \(L=AB + BC\). Substitute \(AB = 7\) and \(BC = 5\) (units, since each unit is 1 kilometer). \(L=7+5=12\) kilometers.

Answer:

D. 12 kilometers