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# 3. Calculate intersection point

## Video transcript

now that you have a feel for how t works we're ready to calculate our intersection point I between our racy P and our line segment a-b recall from the previous video that the slope intercept form of the line a B is y equals negative 3x plus 11 in the parametric representation of the race CP is the function R of T equals 1 minus T times C plus T times P different values of the parameter T locate different points on the Ray the intersection point that we're after is one such point on the Ray so there must be some value of T call it t star such that I equals R of T star this is really two equations one for the x coordinate of I and one for the y coordinate these two equations are I sub x equals R sub X of T star which equals 1 minus T star times C sub X plus T star times P sub X in the same way I sub y equals R sub y of T star which equals 1 minus T star times C sub y plus T star times P sub y in this particular case see our camera position has coordinates 0 0 and P has coordinates 2 1/2 so we have I sub X equals T star times 2 and I sub y equals T star times 1/2 is also on the line segment a-b meaning that i satisfies the slope-intercept form for a B that is y sub y equals negative 3 times I sub X plus 11 so we have three equations in three unknowns I sub X I so Y and T star we can solve the system of equations by substituting the first two equations into the third to get an equation just in T star 1/2 T star equals negative 3 times 2 times T star plus 11 solve this for T star then plug that value of T star into the first two equations to get I sub X and I sub y and that's how it's done before we continue get some experience using this kind of parametric function in the next exercise