For a) is just the distance formula
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for b) is also the distance formula, just different coordinates and distance
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for c) well... we know AB = BC.... we do have the coordinates for A and B
so... find the distance for AB, that is
now.. whatever that is, is = BC, so the distance for BC is
so... whatever distance you get for AB, set it equals to BC, BC will be in "y-terms" since the C point has a variable in its ordered points
so.. .solve AB = BC for "y"
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now d) we know M and N are equidistant to P, that simply means that P is the midpoint of the segment MN
so use the midpoint formula
now, for d), you can also just use the distance formula, find the distance for MP, then since MP = PN, find the distance for PN in x-terms and then set it to equal to MP and solve for "x"
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for b) is also the distance formula, just different coordinates and distance
--------------------------------------------------------------------------
for c) well... we know AB = BC.... we do have the coordinates for A and B
so... find the distance for AB, that is
now.. whatever that is, is = BC, so the distance for BC is
so... whatever distance you get for AB, set it equals to BC, BC will be in "y-terms" since the C point has a variable in its ordered points
so.. .solve AB = BC for "y"
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now d) we know M and N are equidistant to P, that simply means that P is the midpoint of the segment MN
so use the midpoint formula
now, for d), you can also just use the distance formula, find the distance for MP, then since MP = PN, find the distance for PN in x-terms and then set it to equal to MP and solve for "x"