Points and Distance Formula
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PSAT Math › Points and Distance Formula
One line has four collinear points in order from left to right A, B, C, D. If AB = 10’, CD was twice as long as AB, and AC = 25’, how long is AD?
45'
40'
50'
35'
30'
Explanation
AB = 10 ’
BC = AC – AB = 25’ – 10’ = 15’
CD = 2 * AB = 2 * 10’ = 20 ’
AD = AB + BC + CD = 10’ + 15’ + 20’ = 45’
One line has four collinear points in order from left to right A, B, C, D. If AB = 10’, CD was twice as long as AB, and AC = 25’, how long is AD?
45'
40'
50'
35'
30'
Explanation
AB = 10 ’
BC = AC – AB = 25’ – 10’ = 15’
CD = 2 * AB = 2 * 10’ = 20 ’
AD = AB + BC + CD = 10’ + 15’ + 20’ = 45’
What is the distance between (1, 4) and (5, 1)?
4
5
9
3
7
Explanation
Let P1 = (1, 4) and P2 = (5, 1)
Substitute these values into the distance formula:
The distance formula is an application of the Pythagorean Theorem: a2 + b2 = c2
What is the distance between (1, 4) and (5, 1)?
4
5
9
3
7
Explanation
Let P1 = (1, 4) and P2 = (5, 1)
Substitute these values into the distance formula:
The distance formula is an application of the Pythagorean Theorem: a2 + b2 = c2
Points D and E lie on the same line and have the coordinates 
Explanation
The first step is to find the equation of the line that the original points, D and E, are on. You have two points, so you can figure out the slope of the line by plugging the points into the equation
Therefore, you can get an equation in the line in point-slope form, which is
Plug in the answer options, and you will find that only the point 
Points D and E lie on the same line and have the coordinates
Explanation
The first step is to find the equation of the line that the original points, D and E, are on. You have two points, so you can figure out the slope of the line by plugging the points into the equation
Therefore, you can get an equation in the line in point-slope form, which is
Plug in the answer options, and you will find that only the point
What is the distance of the line drawn between points (–1,–2) and (–9,4)?
√5
16
10
4
6
Explanation
The answer is 10. Use the distance formula between 2 points, or draw a right triangle with legs length 6 and 8 and use the Pythagorean Theorem.
What is the distance of the line drawn between points (–1,–2) and (–9,4)?
√5
16
10
4
6
Explanation
The answer is 10. Use the distance formula between 2 points, or draw a right triangle with legs length 6 and 8 and use the Pythagorean Theorem.
What is the distance between the points 
Explanation
Plug the points into the distance formula and simplify:
distance2 = (_x_2 – _x_1)2 + (_y_2 – _y_1)2 = (7 – 3)2 + (2 – 12)2 = 42 + 102 = 116
distance = √116 = √(4 * 29) = 2√29
What is the distance between the points
Explanation
Plug the points into the distance formula and simplify:
distance2 = (_x_2 – _x_1)2 + (_y_2 – _y_1)2 = (7 – 3)2 + (2 – 12)2 = 42 + 102 = 116
distance = √116 = √(4 * 29) = 2√29