So if you check the picture below, each side of the diamond has 90ft, so half-way from first to second is 45ft over the "x" line
a)
in this case, notice that "y" is static, is a constant, it doesn't change, whilst the "r" distance is and the "x" as well, when the runner is going to 1st base
![\bf r^2=x^2+y^2\implies r^2=x^2+90^2\impliedby \textit{since "y" is a constant} \\\\\\ 2r\cfrac{dr}{dt}=2x\cfrac{dx}{dt}+0\implies \cfrac{dr}{dt}=\cfrac{x\frac{dx}{dt}}{r}\quad \begin{cases} x=45\\ \frac{dx}{dt}=19\\ r=45\sqrt{5} \end{cases} \\\\\\ \cfrac{dr}{dt}=\cfrac{19\cdot 45}{45\pm\sqrt{5}}\implies \cfrac{dr}{dt}=-\cfrac{19}{\sqrt{5}}\impliedby \begin{array}{llll} \textit{we used }-\sqrt{5}\\ \textit{because the rate is}\\ negative \end{array}](https://tex.z-dn.net/?f=%5Cbf%20r%5E2%3Dx%5E2%2By%5E2%5Cimplies%20r%5E2%3Dx%5E2%2B90%5E2%5Cimpliedby%20%5Ctextit%7Bsince%20%22y%22%20is%20a%20constant%7D%0A%5C%5C%5C%5C%5C%5C%0A2r%5Ccfrac%7Bdr%7D%7Bdt%7D%3D2x%5Ccfrac%7Bdx%7D%7Bdt%7D%2B0%5Cimplies%20%5Ccfrac%7Bdr%7D%7Bdt%7D%3D%5Ccfrac%7Bx%5Cfrac%7Bdx%7D%7Bdt%7D%7D%7Br%7D%5Cquad%20%0A%5Cbegin%7Bcases%7D%0Ax%3D45%5C%5C%0A%5Cfrac%7Bdx%7D%7Bdt%7D%3D19%5C%5C%0Ar%3D45%5Csqrt%7B5%7D%0A%5Cend%7Bcases%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7Bdr%7D%7Bdt%7D%3D%5Ccfrac%7B19%5Ccdot%2045%7D%7B45%5Cpm%5Csqrt%7B5%7D%7D%5Cimplies%20%5Ccfrac%7Bdr%7D%7Bdt%7D%3D-%5Ccfrac%7B19%7D%7B%5Csqrt%7B5%7D%7D%5Cimpliedby%20%0A%5Cbegin%7Barray%7D%7Bllll%7D%0A%5Ctextit%7Bwe%20used%20%7D-%5Csqrt%7B5%7D%5C%5C%0A%5Ctextit%7Bbecause%20the%20rate%20is%7D%5C%5C%0Anegative%0A%5Cend%7Barray%7D)
b)
well on this case, the distance "y" from home plate to 3rd base, isn't changing either, is a constant and is also 90ft as well