How to downsample x y data?

I have a trajectory that consists of 42 x,y coordinates;

I need to downsample these coordinates into 11 x,y points;

Just wonder if there is a function in R that can do that for me.

the data is :

x-coordinate

x= c(1.07,0.98,0.90,0.81,0.73,0.65,0.57,0.49,0.41,0.33,0.25,0.17,0.1,0.01,-0.06,
     -0.14,-0.21,-0.28,-0.36,-0.43,-0.49,-0.54,-0.59,-0.63,-0.66,-0.69,-0.72,-0.73,
      -0.72,-0.70,-0.67,-0.64,-0.61,-0.63-0.64,-0.65,-0.65,-0.65,-0.65,-0.66,-0.66,
      -0.64)

y-coordinate

y=c(-0.11,-0.09,-0.10,-0.12,-0.13,-0.14,-0.19,-0.21,-0.22,-0.24,-0.26,-0.28,-0.30,
     -0.32,-0.34,-0.37,-0.41,-0.45,-0.50,-0.55,-0.61,-0.68,-0.76,-0.84,-0.92,-1.00,
     -1.08,-1.18,-1.28,-1.38,-1.47,-1.56,-1.61,-1.67,-1.73,-1.79,-1.85,-1.91,-1.96,
     -2.02,-2.07)

The function approx allows you to interpolate values, so assuming your points are measured at regular time intervals, you can downsample the path into 11 regularly measured points along the path as follows:

x2 <- approx(seq(0, 1, length = length(x)), x, xout = seq(0, 1, length = 11))$y
y2 <- approx(seq(0, 1, length = length(y)), y, xout = seq(0, 1, length = 11))$y

Now if you plot the original path:

plot(x, y, type = "l")

Then you can see the 11 downsampled points along the path:

points(x2, y2, col = 'red')