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八年级数学填空题一般
题目
​​先阅读一段文字,再回答下列问题:已知在平面内两点坐标P1(x1P_{1}(x_{1},y1)y_{1}),P2(x2P_{2}(x_{2},y2)y_{2}),其两点间距离公式为:p1p2=(x1x2)2+(y1y2)2p_{1}p_{2}=\sqrt{(x_{1}-x_{2})^{2}+(y_{1}-y_{2})^{2}},例如:点(3,2)\left(3,2\right)(4,0)\left(4,0\right)的距离为(34)2+(20)2=5\sqrt{(3-4)^{2}+(2-0)^{2}}=\sqrt{5}.同时,当两点所在的直线在坐标轴上或平行于xx轴或平行于yy轴距离公式可简化成:p1p2=x1x2p_{1}p_{2}=|x_{1}-x_{2}|p1p2=y1y2p_{1}p_{2}=|y_{1}-y_{2}|.
(1)(1)已知AABB在平行于yy轴的直线上,点AA的纵坐标为55,点BB的纵坐标为22,则AA,BB两点的距离为______;
(2)(2)线段ABAB平行于xx轴,且AB=3AB=3,若点BB的坐标为(2,4)\left(2,4\right),则点AA的坐标是______;
(3)(3)已知A(3,5)A\left(3,5\right),B(4,4)B\left(-4,4\right),AA,BB两点的距离为______;
(4)(4)已知ABC\triangle ABC三个顶点坐标为A(3,4)A\left(3,4\right),B(0,5)B\left(0,5\right),C(1,2)C\left(-1,2\right),请判断此三角形的形状,并说明理由.
知识点:两点间的距离公式I章节:未标注

答案与解析

答案

(1)AB=52=3\left(1\right)AB=5-2=3
故答案为:33
(2)(2)\because线段ABAB平行于xx轴,点BB的坐标为(2,4)\left(2,4\right)
\therefore设点AA的坐标是(a,4)\left(a,4\right)
AB=3\because AB=3
\thereforeAA的横坐标为a2=3|a-2|=3
a=5\therefore a=5a=1a=-1
\thereforeAA的坐标是(5,4)\left(5,4\right)(1,4)\left(-1,4\right)
故答案为:(5,4)\left(5,4\right)(1,4)\left(-1,4\right)
(3)A(3,5),B(4,4)(3)\because A\left(3,5\right),B\left(-4,4\right)
AB=(3+4)2+(54)2=52\therefore AB=\sqrt{(3+4)^{2}+(5-4)^{2}}=5\sqrt{2}
故答案为:525\sqrt{2}
(4)ABC(4)\triangle ABC为等腰直角三角形,理由如下:
A(3,4)\because A\left(3,4\right)B(0,5)B\left(0,5\right)C(1,2)C\left(-1,2\right)
AB=(30)2+(45)2=10\therefore AB=\sqrt{(3-0)^{2}+(4-5)^{2}}=\sqrt{10}
BC=(0+1)2+(52)2=10BC=\sqrt{(0+1)^{2}+(5-2)^{2}}=\sqrt{10}
AC=(3+1)2+(42)2=20=25AC=\sqrt{(3+1)^{2}+(4-2)^{2}}=\sqrt{20}=2\sqrt{5}
AB=AC\therefore AB=ACAB2+BC2=20=AC2AB^{2}+BC^{2}=20=AC^{2}
ABC\therefore \triangle ABC为等腰直角三角形.

解析

(1)AB=52=3\left(1\right)AB=5-2=3
故答案为:33
(2)(2)\because线段ABAB平行于xx轴,点BB的坐标为(2,4)\left(2,4\right)
\therefore设点AA的坐标是(a,4)\left(a,4\right)
AB=3\because AB=3
\thereforeAA的横坐标为a2=3|a-2|=3
a=5\therefore a=5a=1a=-1
\thereforeAA的坐标是(5,4)\left(5,4\right)(1,4)\left(-1,4\right)
故答案为:(5,4)\left(5,4\right)(1,4)\left(-1,4\right)
(3)A(3,5),B(4,4)(3)\because A\left(3,5\right),B\left(-4,4\right)
AB=(3+4)2+(54)2=52\therefore AB=\sqrt{(3+4)^{2}+(5-4)^{2}}=5\sqrt{2}
故答案为:525\sqrt{2}
(4)ABC(4)\triangle ABC为等腰直角三角形,理由如下:
A(3,4)\because A\left(3,4\right)B(0,5)B\left(0,5\right)C(1,2)C\left(-1,2\right)
AB=(30)2+(45)2=10\therefore AB=\sqrt{(3-0)^{2}+(4-5)^{2}}=\sqrt{10}
BC=(0+1)2+(52)2=10BC=\sqrt{(0+1)^{2}+(5-2)^{2}}=\sqrt{10}
AC=(3+1)2+(42)2=20=25AC=\sqrt{(3+1)^{2}+(4-2)^{2}}=\sqrt{20}=2\sqrt{5}
AB=AC\therefore AB=ACAB2+BC2=20=AC2AB^{2}+BC^{2}=20=AC^{2}
ABC\therefore \triangle ABC为等腰直角三角形.

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