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# Core 1 Help watch

1. I need help with some core 1 work please, question is below;

14 (a) Find the equation of the line l through the point A(2,3) with gradient -1/2
(b) Show that the point P with coordinates (2+2t, 3-t) will always lie on l whatever the value of t.
(c) Find the values of t such that the length AP is 5 units.
(d) Find the value of t such that OP is perpendicular to l (where O is the origin). Hence find the length of the perpendicular from O to l.

I have completed parts (a) - (c) with the correct answers but please could you help with part (d).

Thanks
2. The key point here is that in part b you know the set of point on l.
You also know that two perpendicular gradients multiply to give -1.
You have a point and the origin hence you can find the length
3. (Original post by hannahguze99)
I need help with some core 1 work please, question is below;

14 (a) Find the equation of the line l through the point A(2,3) with gradient -1/2
(b) Show that the point P with coordinates (2+2t, 3-t) will always lie on l whatever the value of t.
(c) Find the values of t such that the length AP is 5 units.
(d) Find the value of t such that OP is perpendicular to l (where O is the origin). Hence find the length of the perpendicular from O to l.

I have completed parts (a) - (c) with the correct answers but please could you help with part (d).

Thanks
For part (d) you know the line OP is perpendicular to the line l. What does this tell you about the gradient of OP?

Once you've got the gradient, you also know it passes through the point (0,0). Hope I've given enough of a hint
4. Thank you both for your help

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