Question

Can someone help me with this please? I'll give extra points :(

Answer 1

Distance between points K and L = 9 units

Distance between points M and N = √1282 or approximately 35.805 units

Explanation:

We can find the distance, d, between a pair of points using the distance formula, which is

`d=\sqrt{(x_(2)-x_(1))^2+(y_(2)-y_(1))^2}`, where (x1, y1) are set of points, and (x2, y2) are another set.

Distance between K and L:

We can allow K (5, 0) to be our (x1, y1) point and L (-4, 0) to be our (x2, y2) point. Now we can plug in the points into the distance formula:

`d=√((5-(-4))^2+(0-0)^2)\\ d=√(9^2)\\ d=√(81)\\ d=9`

Thus, the distance between points K and L is 9 units

• If you were to use graphing paper, you would see that the points both lie on the x-axis and you counting the ticks between the two points would show that they are 9 units apart

Distance between M and N:

Now, can allow M (-21, -29) to be our (x1, y1) point and N (0, 0) to be our (x2, y2) point. Now we can plug in the points into the distance formula:

`d=√((-21-0)^2+(-29-0)^2)\\ d=√((-21)^2+(-29)^2)\\ d=√(441+841)\\ d=√(1282) \\d=35.80502758\\d=35.805`

sqrt (1282) is the exact distance between the two points, while 35.805 is the approximate distance between the two points to the nearest thousandth

• On graphing paper, the points would look about 35 units apart, but the distance formula allows us to be more exact since 35^2 is 1225 and this is 57 less than 1282