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Distances & Areas practice questions — SAT Math

12 free multiple-choice problems on distances & areas, ordered to match SAT Math difficulty, each with a full worked solution. No account needed — and there's a fresh problem set every day.

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Problem #0930 US SAT
Beginnergeometry
The distance between and is:

Problems & worked solutions

Problem #0930 US SAT

Problem 1 — Distances & Areas

The distance between A=(1,2) and B=(4,6) is:

Show answer & worked solution
  1. A. 4
  2. B. 5✓ correct
  3. C. 7
  4. D. 25

AB=(4−1)2+(6−2)2=9+16=25=5.

Problem #0937 US SAT

Problem 2 — Distances & Areas

The area of a triangle with base 10 and height 6 is:

Show answer & worked solution
  1. A. 60
  2. B. 30✓ correct
  3. C. 16
  4. D. 15

A=12⋅10⋅6=30.

Problem #0231 International

Problem 3 — Distances & Areas

The distance between A(1,2) and B(4,6) is:

Show answer & worked solution
  1. A. 3
  2. B. 4
  3. C. 5✓ correct
  4. D. 7

d=(4−1)2+(6−2)2=9+16=5.

Problem #0232 International

Problem 4 — Distances & Areas

The midpoint of segment AB where A(2,4) and B(8,10) is:

Show answer & worked solution
  1. A. (3,5)
  2. B. (4,6)
  3. C. (5,7)✓ correct
  4. D. (6,14)

M= ⁣(102, 142)=(5,7).

Problem #0233 International

Problem 5 — Distances & Areas

The area of the rectangle with vertices A(0,0),B(5,0),C(5,3),D(0,3) is:

Show answer & worked solution
  1. A. 8
  2. B. 10
  3. C. 15✓ correct
  4. D. 30

Width =5, height =3. Area =15.

Problem #0234 International

Problem 6 — Distances & Areas

A triangle has vertices A(0,0), B(6,0), C(0,4). Its area equals:

Show answer & worked solution
  1. A. 6
  2. B. 10
  3. C. 12✓ correct
  4. D. 24

Base =6, height =4. Area =12⋅6⋅4=12.

Problem #0235 International

Problem 7 — Distances & Areas

The area of the triangle with vertices A(1,1), B(4,5), C(7,2) is:

Show answer & worked solution
  1. A. 152
  2. B. 9
  3. C. 212✓ correct
  4. D. 15

Area=12 ∣1(5−2)+4(2−1)+7(1−5)∣=12 ∣3+4−28∣=12⋅21=212.

Problem #0237 International

Problem 8 — Distances & Areas

The points A(1,2), B(3,6), C(5,10) are:

Show answer & worked solution
  1. A. collinear✓ correct
  2. B. vertices of a right triangle
  3. C. vertices of an isosceles triangle
  4. D. vertices of an equilateral triangle

Area =12 ∣1(6−10)+3(10−2)+5(2−6)∣=12 ∣−4+24−20∣=0. Hence collinear.

Problem #0236 International

Problem 9 — Distances & Areas

The distance from the origin to the point P(−3,4) is:

Show answer & worked solution
  1. A. 1
  2. B. 5✓ correct
  3. C. 7
  4. D. 25

d=(−3)2+42=25=5.

Problem #0238 International

Problem 10 — Distances & Areas

The perimeter of the triangle with vertices A(0,0), B(3,0), C(0,4) is:

Show answer & worked solution
  1. A. 7
  2. B. 10
  3. C. 12✓ correct
  4. D. 20

∣AB∣=3, ∣AC∣=4, ∣BC∣=9+16=5. Perimeter =3+4+5=12.

2 more Distances & Areas questions in the app

Also covered in Distances & Areas practice across every exam.

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