Canada Grade 8 Coordinate geometry

• 5 units

• 6 units

• 7 units

• 8 units

Answer explanation

To find the distance between points (3, 4) and (7, 1), use the distance formula: \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\). Plugging in the values gives \(d = \sqrt{(7 - 3)^2 + (1 - 4)^2} = \sqrt{16 + 9} = \sqrt{25} = 5\) units.

Answer explanation

To check which point lies on the line y = 2x + 3, substitute the x-value into the equation. For (0, 3): y = 2(0) + 3 = 3. This matches the y-value of the point. Thus, (0, 3) is the correct answer.

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• 2

• 3

• 4

Answer explanation

To find the slope (m) between points (2, 3) and (4, 7), use the formula m = (y2 - y1) / (x2 - x1). Here, m = (7 - 3) / (4 - 2) = 4 / 2 = 2. Thus, the slope of the line is 2.

Answer explanation

The slope of a line perpendicular to another is the negative reciprocal of the original slope. The slope given is -3/4, so the negative reciprocal is 4/3. Thus, the slope of the perpendicular line is \(\frac{4}{3}\).

Answer explanation

To find the midpoint of the points (6, 8) and (10, 12), use the formula: ((x1 + x2)/2, (y1 + y2)/2). This gives ((6 + 10)/2, (8 + 12)/2) = (8, 10). Thus, the correct answer is (8, 10).

Answer explanation

Lines that are parallel have the same slope. The slope of the given line, y = -2x + 5, is -2. The equation y = -2x + 3 also has a slope of -2, making it parallel. The other options have different slopes.

Answer explanation

To find the equation of the line, use the point-slope form: y - y1 = m(x - x1). Here, m = 3 and (x1, y1) = (1, 2). Plugging in, we get y - 2 = 3(x - 1), which simplifies to y = 3x - 1.

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• 4

Answer explanation

To find x, substitute y = 4 into the equation y = 2x + 2. This gives 4 = 2x + 2. Solving for x, we get 2 = 2x, thus x = 1. Therefore, the value of x is 1.

Answer explanation

To find the reflection of the point (3, 5) over the x-axis, we change the sign of the y-coordinate. Thus, (3, 5) reflects to (3, -5), making (3, -5) the correct answer.

• 3

• -3

• 4

• -4

Answer explanation

To find the y-intercept, set x = 0 in the equation 3x - 4y = 12. This gives -4y = 12, so y = -3. Thus, the y-intercept is -3.