point x (6,4) and y (-4,-16) are the endpoint of XY. what are the coordinates of point Z on XY such that XZ is 4/5 the length of XY a) (4,0) b) (0,-8) c) (1,-6) d) (-2,-12)

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point x (6,4) and y (-4,-16) are the endpoint of XY. what are the coordinates of point Z on XY such that XZ is 4/5 the length of XY a) (4,0) b) (0,-8) c) (1,-6) d) (-2,-12)

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distance is \[d=\sqrt{(x _{2}-x _{1})^{2}+(y _{2}-y _{1})^2}\] d= sqrt (-4-6)^2 + (-16-4)^2 d= sqrt (-10)^2 + (-20)^2 d= sqrt 100+400 d=sqrt 500 d=22.36 The distance from point x to point y is about 22.36. 4/5 of this distance is 17.888 (.8 * 22.26) So the distance from X to Z has to be 17.888 17.888=sqrt (x2-6)^2 + (y2-4)^2 you can guestimate from here with the answer choices looking at the graph, you know Z will be closer to Y.|dw:1442530338070:dw| you can also guess that the coordinates of z will both be negative from the graph. so lets try the coordinate (-2,-12 from your options) 17.88=sqrt(-2-6)^2 + (-12-4)^2 17.88=sqrt (-8)^2 + (-16)^2 17.88= sqrt 64+256 17.88= sqrt320 17.88=17.88 this is a true statement. D is your answer
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